Is (5,−1) a solution to the system of these linear equations: x+y=4 and 2x+3y=7? Why?(1 point)
Responses
Yes, because the graphs intersect at (5,−1).
Yes, because the graphs intersect at left parenthesis 5 comma negative 1 right parenthesis .
No, because the graphs don’t intersect at (5,−1).
No, because the graphs don’t intersect at left parenthesis 5 comma negative 1 right parenthesis .
Yes, because the graphs don’t intersect at (5,−1).
Yes, because the graphs don’t intersect at left parenthesis 5 comma negative 1 right parenthesis .
No, because the graphs intersect at (5,−1).
23 answers
Yes, because the graphs intersect at (5,−1).
The point (0,-2) is a solution to which system?
(1 point)
Responses
x + y = 2
-x + 2y = 16
x + y = 2 -x + 2y = 16
-5x + y = -2
-3x + 6y = -12
-5x + y = -2 -3x + 6y = -12
-5x = y - 3
3x - 8y = 24
-5x = y - 3 3x - 8y = 24
-4x + y = 6
-5x - y = 21
-4x + y = 6 -5x - y = 21
(1 point)
Responses
x + y = 2
-x + 2y = 16
x + y = 2 -x + 2y = 16
-5x + y = -2
-3x + 6y = -12
-5x + y = -2 -3x + 6y = -12
-5x = y - 3
3x - 8y = 24
-5x = y - 3 3x - 8y = 24
-4x + y = 6
-5x - y = 21
-4x + y = 6 -5x - y = 21
The point (0, -2) is a solution to the system of equations:
1) x + y = 2
2) -x + 2y = 16
We can check by substituting x = 0 and y = -2 into both equations:
For the first equation:
0 + (-2) = 2
-2 = 2 (not satisfied)
For the second equation:
-(0) + 2(-2) = 16
-4 = 16 (not satisfied)
Since neither equation is satisfied when we substitute (0, -2), (0, -2) is not a solution to the system of equations.
1) x + y = 2
2) -x + 2y = 16
We can check by substituting x = 0 and y = -2 into both equations:
For the first equation:
0 + (-2) = 2
-2 = 2 (not satisfied)
For the second equation:
-(0) + 2(-2) = 16
-4 = 16 (not satisfied)
Since neither equation is satisfied when we substitute (0, -2), (0, -2) is not a solution to the system of equations.
Judy has $100 and Elenore has $75. Judy is saving $5 per day and Elenore is saving $7 per day. (4 points)
What equation represent how much money Judy will have in total after saving for d days? _________
What equation represents how much money Elenore will have in total after saving for d days? _________
What equation would be used to find out how many days it will take for Judy and Elenore to have the same amount of money saved? __________
After the number of days it took both to have the same amount of money saved, how much money do they have each? ________
What equation represent how much money Judy will have in total after saving for d days? _________
What equation represents how much money Elenore will have in total after saving for d days? _________
What equation would be used to find out how many days it will take for Judy and Elenore to have the same amount of money saved? __________
After the number of days it took both to have the same amount of money saved, how much money do they have each? ________
The equation that represents how much money Judy will have in total after saving for d days is:
Judy's total money = $100 + $5 * d
The equation that represents how much money Elenore will have in total after saving for d days is:
Elenore's total money = $75 + $7 * d
The equation that would be used to find out how many days it will take for Judy and Elenore to have the same amount of money saved is:
Judy's total money = Elenore's total money
$100 + $5 * d = $75 + $7 * d
After the number of days it took for both to have the same amount of money saved, the amount of money they each have can be determined by substituting the value of d into either equation.
Judy's total money = $100 + $5 * d
The equation that represents how much money Elenore will have in total after saving for d days is:
Elenore's total money = $75 + $7 * d
The equation that would be used to find out how many days it will take for Judy and Elenore to have the same amount of money saved is:
Judy's total money = Elenore's total money
$100 + $5 * d = $75 + $7 * d
After the number of days it took for both to have the same amount of money saved, the amount of money they each have can be determined by substituting the value of d into either equation.
How could you check to see if the point (5, 6) is the solution to the Linear System of equations?(1 point)
Responses
Substitute 6 in for x and 5 in for y in both of the equations to see if both equations are true.
Substitute 6 in for x and 5 in for y in both of the equations to see if both equations are true.
Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.
Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.
Substitute 5 in for x and 6 in for y in one of the equations to see if the equation is true.
Substitute 5 in for x and 6 in for y in one of the equations to see if the equation is true.
Substitute 6 in for x and 5 in for y in one of the equations to see if the equation is true.
Responses
Substitute 6 in for x and 5 in for y in both of the equations to see if both equations are true.
Substitute 6 in for x and 5 in for y in both of the equations to see if both equations are true.
Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.
Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.
Substitute 5 in for x and 6 in for y in one of the equations to see if the equation is true.
Substitute 5 in for x and 6 in for y in one of the equations to see if the equation is true.
Substitute 6 in for x and 5 in for y in one of the equations to see if the equation is true.
To check if the point (5, 6) is a solution to the Linear System of equations, we need to substitute 5 for x and 6 for y in both of the equations to see if both equations are true. So the correct response is:
Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.
Substitute 5 in for x and 6 in for y in both of the equations to see if both equations are true.
You are running a concession stand at a baseball game.
You are selling pizza slices and sodas.
Each pizza slice sells for $3.50 and each soda sells for $1.50.
At the end of the night, you made a total of $800.
You sold a total of 344 pizza slices and sodas combined.
You must report the number of pizza slices sold and the number of sodas sold.
What equations did you use to solve this, where P = the number of pizza slices sold and S = the number of sodas sold?
(1 point)
Responses
3.50P + S = 800 and P + 1.50S = 344
3.50P + S = 800 and P + 1.50S = 344
3.50P + 1.50S = 800 and P + S = 344
3.50P + 1.50S = 800 and P + S = 344
3.50S + 1.50P = 800 and P + S = 344
3.50S + 1.50P = 800 and P + S = 344
3.50S + 1.50P = 344 and P + S = 800
You are selling pizza slices and sodas.
Each pizza slice sells for $3.50 and each soda sells for $1.50.
At the end of the night, you made a total of $800.
You sold a total of 344 pizza slices and sodas combined.
You must report the number of pizza slices sold and the number of sodas sold.
What equations did you use to solve this, where P = the number of pizza slices sold and S = the number of sodas sold?
(1 point)
Responses
3.50P + S = 800 and P + 1.50S = 344
3.50P + S = 800 and P + 1.50S = 344
3.50P + 1.50S = 800 and P + S = 344
3.50P + 1.50S = 800 and P + S = 344
3.50S + 1.50P = 800 and P + S = 344
3.50S + 1.50P = 800 and P + S = 344
3.50S + 1.50P = 344 and P + S = 800
The correct equations to represent the scenario are:
3.50P + 1.50S = 800 (equation representing the total revenue from selling pizza slices and sodas)
P + S = 344 (equation representing the total number of pizza slices and sodas sold)
Therefore, the correct response is: 3.50P + 1.50S = 800 and P + S = 344.
3.50P + 1.50S = 800 (equation representing the total revenue from selling pizza slices and sodas)
P + S = 344 (equation representing the total number of pizza slices and sodas sold)
Therefore, the correct response is: 3.50P + 1.50S = 800 and P + S = 344.
Check all that apply. Select the statement(s) that correctly describes the solution to this system of equations:
8x−2y=−4
4x−y=−2
(2 points)
Responses
Solve this system by elimination since it is already in standard form and lined up nicely.
Solve this system by elimination since it is already in standard form and lined up nicely.
There is exactly one solution to this system of linear equations and it is (2, 0).
There is exactly one solution to this system of linear equations and it is (2, 0).
There are infinite solutions to this system of linear equations.
There are infinite solutions to this system of linear equations.
These lines are parallel, so there is no solution to this system of linear equations.
These lines are parallel, so there is no solution to this system of linear equations.
There is exactly one solution to this system of linear equations and it is (0, -2).
There is exactly one solution to this system of linear equations and it is (0, -2).
Solve this system by substitution since one of the variables is defined by the other without having to do any math.
8x−2y=−4
4x−y=−2
(2 points)
Responses
Solve this system by elimination since it is already in standard form and lined up nicely.
Solve this system by elimination since it is already in standard form and lined up nicely.
There is exactly one solution to this system of linear equations and it is (2, 0).
There is exactly one solution to this system of linear equations and it is (2, 0).
There are infinite solutions to this system of linear equations.
There are infinite solutions to this system of linear equations.
These lines are parallel, so there is no solution to this system of linear equations.
These lines are parallel, so there is no solution to this system of linear equations.
There is exactly one solution to this system of linear equations and it is (0, -2).
There is exactly one solution to this system of linear equations and it is (0, -2).
Solve this system by substitution since one of the variables is defined by the other without having to do any math.
The correct statement that describes the solution to this system of equations is:
There is exactly one solution to this system of linear equations and it is (2, 0).
There is exactly one solution to this system of linear equations and it is (2, 0).
Jim bought some potted plants:
Petunias cost $11 per pot and Begonias cost $15 per pot.
Jim bought 19 potted plants in all and spent a total of $225 on the plants.
Which would be a correct statement?
(1 point)
Responses
Jim bought 4 petunias.
Jim bought 4 petunias.
Jim bought 15 begonias.
Jim bought 15 begonias.
Jim bought 18 begonias.
Jim bought 18 begonias.
Jim bought 15 petunias.
Petunias cost $11 per pot and Begonias cost $15 per pot.
Jim bought 19 potted plants in all and spent a total of $225 on the plants.
Which would be a correct statement?
(1 point)
Responses
Jim bought 4 petunias.
Jim bought 4 petunias.
Jim bought 15 begonias.
Jim bought 15 begonias.
Jim bought 18 begonias.
Jim bought 18 begonias.
Jim bought 15 petunias.
To determine the correct statement, we need to set up a system of equations based on the given information.
Let p be the number of petunias and b be the number of begonias.
From the given information, we can set up the following equations:
1) p + b = 19 (equation representing the total number of potted plants Jim bought)
2) 11p + 15b = 225 (equation representing the total cost Jim spent on the plants)
To solve this system, we can use substitution or elimination. However, since none of the given options match the correct solution involving both petunias and begonias, it suggests that there might be a mistake in the question. Please note that the correct statement cannot be determined based on the given options.
Let p be the number of petunias and b be the number of begonias.
From the given information, we can set up the following equations:
1) p + b = 19 (equation representing the total number of potted plants Jim bought)
2) 11p + 15b = 225 (equation representing the total cost Jim spent on the plants)
To solve this system, we can use substitution or elimination. However, since none of the given options match the correct solution involving both petunias and begonias, it suggests that there might be a mistake in the question. Please note that the correct statement cannot be determined based on the given options.
What is the answer
Apologies for any confusion. To determine the correct statement, we can solve the system of equations:
1) p + b = 19
2) 11p + 15b = 225
Multiplying equation 1 by 11, we get:
11p + 11b = 209
Subtracting this equation from equation 2, we get:
11p + 15b - (11p + 11b) = 225 - 209
4b = 16
b = 4
Substituting b = 4 into equation 1, we get:
p + 4 = 19
p = 15
Therefore, the correct statement is: Jim bought 15 petunias.
1) p + b = 19
2) 11p + 15b = 225
Multiplying equation 1 by 11, we get:
11p + 11b = 209
Subtracting this equation from equation 2, we get:
11p + 15b - (11p + 11b) = 225 - 209
4b = 16
b = 4
Substituting b = 4 into equation 1, we get:
p + 4 = 19
p = 15
Therefore, the correct statement is: Jim bought 15 petunias.
To solve this system, you could do the following steps:
3x+4y=48
6x+2y=60
(6 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
1. Choose the best method to solve by looking at the way the equations are set up for you: Response area
2. Using the best method, how could you get the x variables to cancel out? Response area
3. After you complete step 2, what would your top equation be? Response area
4. Line them up and add the equations together to get this equation. Response area
5. Solve for y. Response area
6. Solve for x. Response area
3x+4y=48
6x+2y=60
(6 points)
Put responses in the correct input to answer the question. Select a response, navigate to the desired input and insert the response. Responses can be selected and inserted using the space bar, enter key, left mouse button or touchpad. Responses can also be moved by dragging with a mouse.
1. Choose the best method to solve by looking at the way the equations are set up for you: Response area
2. Using the best method, how could you get the x variables to cancel out? Response area
3. After you complete step 2, what would your top equation be? Response area
4. Line them up and add the equations together to get this equation. Response area
5. Solve for y. Response area
6. Solve for x. Response area
1. Choose the best method to solve by looking at the way the equations are set up for you:
The best method to solve this system of equations is by using elimination since the coefficients of either the x or y term can easily be made the same by multiplying one or both of the equations.
2. Using the best method, how could you get the x variables to cancel out?
To cancel out the x variables, you can multiply equation 1 by 2 and multiply equation 2 by 3 to make the coefficients of the x term the same.
3. After you complete step 2, what would your top equation be?
When you multiply equation 1 by 2, you get: 6x + 8y = 96.
4. Line them up and add the equations together to get this equation.
When you add the new equation (6x + 8y = 96) to equation 2 (6x + 2y = 60), you get: 12x + 10y = 156.
5. Solve for y.
Divide the equation 12x + 10y = 156 by 10 to solve for y: y = (156 - 12x)/10.
6. Solve for x.
To solve for x, substitute the expression for y in equation 1:
3x + 4[(156 - 12x)/10] = 48.
Simplify and solve for x.
The best method to solve this system of equations is by using elimination since the coefficients of either the x or y term can easily be made the same by multiplying one or both of the equations.
2. Using the best method, how could you get the x variables to cancel out?
To cancel out the x variables, you can multiply equation 1 by 2 and multiply equation 2 by 3 to make the coefficients of the x term the same.
3. After you complete step 2, what would your top equation be?
When you multiply equation 1 by 2, you get: 6x + 8y = 96.
4. Line them up and add the equations together to get this equation.
When you add the new equation (6x + 8y = 96) to equation 2 (6x + 2y = 60), you get: 12x + 10y = 156.
5. Solve for y.
Divide the equation 12x + 10y = 156 by 10 to solve for y: y = (156 - 12x)/10.
6. Solve for x.
To solve for x, substitute the expression for y in equation 1:
3x + 4[(156 - 12x)/10] = 48.
Simplify and solve for x.
Both of these tables represent linear graphs:
Does the line through the first set of points intersect with the line through the second set of points?
(1 point)
Responses
You cannot tell without a graph
You cannot tell without a graph
Yes…these lines are parallel
Yes…these lines are parallel
No…these lines are perpendicular
No…these lines are perpendicular
Yes…these lines are perpendicular
Yes…these lines are perpendicular
Yes…these lines are not parallel nor perpendicular
Yes…these lines are not parallel nor perpendicular
No…these lines are parallel
Does the line through the first set of points intersect with the line through the second set of points?
(1 point)
Responses
You cannot tell without a graph
You cannot tell without a graph
Yes…these lines are parallel
Yes…these lines are parallel
No…these lines are perpendicular
No…these lines are perpendicular
Yes…these lines are perpendicular
Yes…these lines are perpendicular
Yes…these lines are not parallel nor perpendicular
Yes…these lines are not parallel nor perpendicular
No…these lines are parallel
You cannot tell without a graph.
Does the line through (3, 7) and (-2, -5) intersect with the line through (4, 8) and (10, -2)?(1 point)
Responses
Yes…these lines are parallel
Yes…these lines are parallel
No…these lines are parallel
No…these lines are parallel
No…these lines are perpendicular
No…these lines are perpendicular
Yes…these lines are not parallel
Yes…these lines are not parallel
You cannot tell without a graph
You cannot tell without a graph
Yes…these lines are perpendicular
Responses
Yes…these lines are parallel
Yes…these lines are parallel
No…these lines are parallel
No…these lines are parallel
No…these lines are perpendicular
No…these lines are perpendicular
Yes…these lines are not parallel
Yes…these lines are not parallel
You cannot tell without a graph
You cannot tell without a graph
Yes…these lines are perpendicular
You cannot tell without a graph.
A student claims that hitting a tennis ball across the court is an example of balanced forces. Is he correct?(1 point)
Responses
Yes, because the force in the direction of the ball’s motion is greater.
Yes, because the force in the direction of the ball’s motion is greater.
No, because equal forces act on the ball from all sides.
No, because equal forces act on the ball from all sides.
No, because the force in the direction of the ball’s motion is greater.
No, because the force in the direction of the ball’s motion is greater.
Yes, because equal forces act on the ball from all sides.
Responses
Yes, because the force in the direction of the ball’s motion is greater.
Yes, because the force in the direction of the ball’s motion is greater.
No, because equal forces act on the ball from all sides.
No, because equal forces act on the ball from all sides.
No, because the force in the direction of the ball’s motion is greater.
No, because the force in the direction of the ball’s motion is greater.
Yes, because equal forces act on the ball from all sides.
No, because equal forces act on the ball from all sides.
1 answer