The solution to a system of two linear equations is x = 3 weeks; y = 9 feet
Match the description with the correct statement.
(3 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.
The solution to this system could possibly have this meaning.
17 answers
The solution to the system of equations represents that 3 weeks have passed and the height reached is 9 feet.
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 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.
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 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.
Responses
Substitute 6 in for x and 5 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.
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 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 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
3.50S + 1.50P = 344 and P + S = 800
3.50S + 1.50P = 344 and P + S = 800
3.50S + 1.50P = 800 and P + S = 344
3.50S + 1.50P = 800 and P + S = 344
3.50P + 1.50S = 800 and P + S = 344
3.50P + 1.50S = 800 and P + S = 344
3.50P + S = 800 and P + 1.50S = 344
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
3.50S + 1.50P = 344 and P + S = 800
3.50S + 1.50P = 344 and P + S = 800
3.50S + 1.50P = 800 and P + S = 344
3.50S + 1.50P = 800 and P + S = 344
3.50P + 1.50S = 800 and P + S = 344
3.50P + 1.50S = 800 and P + S = 344
3.50P + S = 800 and P + 1.50S = 344
3.50S + 1.50P = 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.
There is exactly one solution to this system of linear equations and it is (2, 0).
is that all that apply?
My apologies for missing that.
The correct statements that describe the solution to this system of equations are:
- There is exactly one solution to this system of linear equations and it is (2, 0).
- Solve this system by elimination since it is already in standard form and lined up nicely.
The correct statements that describe the solution to this system of equations are:
- There is exactly one solution to this system of linear equations and it is (2, 0).
- Solve this system by elimination since it is already in standard form and lined up nicely.
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 15 petunias.
Jim bought 15 petunias.
Jim bought 18 begonias.
Jim bought 18 begonias.
Jim bought 4 petunias.
Jim bought 4 petunias.
Jim bought 15 begonias.
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 15 petunias.
Jim bought 15 petunias.
Jim bought 18 begonias.
Jim bought 18 begonias.
Jim bought 4 petunias.
Jim bought 4 petunias.
Jim bought 15 begonias.
Jim bought 15 petunias.
Solve the system of equations graphically. You can use your graphing calculator!
y=−2x−1
3x − y =−7
(1 point)
Responses
Solution is (-1, -1)
Solution is (-1, -1)
Solution is (0, 2)
Solution is (0, 2)
Solution is (-1.5, 0)
Solution is (-1.5, 0)
Solution is (-1.6, 2.2 )
y=−2x−1
3x − y =−7
(1 point)
Responses
Solution is (-1, -1)
Solution is (-1, -1)
Solution is (0, 2)
Solution is (0, 2)
Solution is (-1.5, 0)
Solution is (-1.5, 0)
Solution is (-1.6, 2.2 )
The correct statement is: Solution is (-1, -1)
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
Choose a method
Operation to get the x variables to cancel
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
Choose a method
Operation to get the x variables to cancel
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 the elimination method since the coefficients of the x or y terms can be easily made to cancel out.
Using the best method, how could you get the x variables to cancel out?
- To cancel out the x variables, you can multiply the first equation by 2 and the second equation by 3. This will make the coefficients of the x terms equal in magnitude but opposite in sign.
After you complete step 2, what would your top equation be?
- After multiplying the first equation by 2, the top equation becomes:
6x + 8y = 96
Line them up and add the equations together to get this equation.
- 3x + 4y = 48
+ 6x + 8y = 96
---------------
9x + 12y = 144
Solve for y.
- Dividing both sides of the equation 9x + 12y = 144 by 12, we get:
y = 12 - (3/4)x
Solve for x.
- To solve for x, substitute the value of y back into one of the original equations and solve for x.
- The best method to solve this system of equations is by using the elimination method since the coefficients of the x or y terms can be easily made to cancel out.
Using the best method, how could you get the x variables to cancel out?
- To cancel out the x variables, you can multiply the first equation by 2 and the second equation by 3. This will make the coefficients of the x terms equal in magnitude but opposite in sign.
After you complete step 2, what would your top equation be?
- After multiplying the first equation by 2, the top equation becomes:
6x + 8y = 96
Line them up and add the equations together to get this equation.
- 3x + 4y = 48
+ 6x + 8y = 96
---------------
9x + 12y = 144
Solve for y.
- Dividing both sides of the equation 9x + 12y = 144 by 12, we get:
y = 12 - (3/4)x
Solve for x.
- To solve for x, substitute the value of y back into one of the original equations and solve for x.
so what is x
To determine the value of x, we need to substitute the expression for y back into one of the original equations. Let's use the first equation:
3x + 4y = 48
Substituting y = 12 - (3/4)x, we have:
3x + 4(12 - (3/4)x) = 48
Expanding and simplifying:
3x + 48 - 3x = 48
The x terms cancel out:
48 = 48
This equation is true regardless of the value of x. Therefore, x can be any real number.
3x + 4y = 48
Substituting y = 12 - (3/4)x, we have:
3x + 4(12 - (3/4)x) = 48
Expanding and simplifying:
3x + 48 - 3x = 48
The x terms cancel out:
48 = 48
This equation is true regardless of the value of x. Therefore, x can be any real number.