To determine which system the point (0, -2) is a solution to, you can substitute the x and y values into each equation and see which ones make the statement true.
Option 1: -5x = y - 3
Substituting x = 0 and y = -2 gives:
-5(0) = -2 - 3
0 = -2 - 3
0 ≠ -5
Option 2: 3x - 8y = 24
Substituting x = 0 and y = -2 gives:
3(0) - 8(-2) = 24
16 = 24
16 ≠ 24
Option 3: -4x + y = 6
Substituting x = 0 and y = -2 gives:
-4(0) + (-2) = 6
-2 = 6
-2 ≠ 6
Option 4: -5x - y = 21
Substituting x = 0 and y = -2 gives:
-5(0) - (-2) = 21
2 = 21
2 ≠ 21
Option 5: -5x + y = -2
Substituting x = 0 and y = -2 gives:
-5(0) + (-2) = -2
-2 = -2
-2 = -2
Option 6: -3x + 6y = -12
Substituting x = 0 and y = -2 gives:
-3(0) + 6(-2) = -12
-12 = -12
-12 = -12
Option 7: x + y = 2
Substituting x = 0 and y = -2 gives:
0 + (-2) = 2
-2 = 2
-2 ≠ 2
Option 8: -x + 2y = 16
Substituting x = 0 and y = -2 gives:
-(0) + 2(-2) = 16
-4 = 16
-4 ≠ 16
Based on the substitutions, the point (0, -2) is a solution to the system:
-5x + y = -2
-3x + 6y = -12
Remember: You can use your graphing calculator!
The point (0,-2) is a solution to which system?
(1 point)
Responses
-5x = y - 3
3x - 8y = 24
-5x = y - 3 3x - 8y = 24
-4x + y = 6
-5x - y = 21
-4x + y = 6 -5x - y = 21
-5x + y = -2
-3x + 6y = -12
-5x + y = -2 -3x + 6y = -12
x + y = 2
-x + 2y = 16
5 answers
Match the system of equations to the number of solutions it has.
You can use your Graphing Calculator!
(4 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.
y = 5x + 7
3y - 15x = 18
y = 3x + 6
y = -13x - 4
x - 2y = 6
3x - 6y = 18
y = 23x - 1
y = 23x - 2
You can use your Graphing Calculator!
(4 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.
y = 5x + 7
3y - 15x = 18
y = 3x + 6
y = -13x - 4
x - 2y = 6
3x - 6y = 18
y = 23x - 1
y = 23x - 2
To determine the number of solutions each system of equations has, we can analyze the equations and look for patterns or relationships.
System 1: y = 5x + 7
This is a linear equation with a slope of 5 and a y-intercept of 7. Since it is a linear equation, it will have infinitely many solutions, as every point on the line y = 5x + 7 is a solution to the equation.
System 2: 3y - 15x = 18
This is also a linear equation, but it is not in slope-intercept form. To determine the number of solutions, we can rearrange it into slope-intercept form:
3y = 15x + 18
y = 5x + 6
This equation has the same form as System 1, so it also has infinitely many solutions.
System 3: y = 3x + 6
This is another linear equation with a slope of 3 and a y-intercept of 6. Like the previous equations, it has infinitely many solutions.
System 4: y = -13x - 4
This linear equation has a slope of -13 and a y-intercept of -4. Again, it has infinitely many solutions.
System 5: x - 2y = 6
This equation is linear as well, but it is not in slope-intercept form. To determine the number of solutions, we can rearrange it:
2y = x - 6
y = (1/2)x - 3
This equation has the same form as System 1 and System 3, so it also has infinitely many solutions.
System 6: 3x - 6y = 18
This equation can be rearranged into slope-intercept form:
-6y = -3x + 18
y = (1/2)x - 3
Again, it has the same form as System 1 and System 3, so it has infinitely many solutions.
System 7: y = 23x - 1
This linear equation has a slope of 23 and a y-intercept of -1. Once again, it has infinitely many solutions.
System 8: y = 23x - 2
This equation is similar to System 7; it also has a slope of 23 and a y-intercept of -2. Thus, it has infinitely many solutions.
Based on the above analysis, all of the systems of equations have infinitely many solutions.
System 1: y = 5x + 7
This is a linear equation with a slope of 5 and a y-intercept of 7. Since it is a linear equation, it will have infinitely many solutions, as every point on the line y = 5x + 7 is a solution to the equation.
System 2: 3y - 15x = 18
This is also a linear equation, but it is not in slope-intercept form. To determine the number of solutions, we can rearrange it into slope-intercept form:
3y = 15x + 18
y = 5x + 6
This equation has the same form as System 1, so it also has infinitely many solutions.
System 3: y = 3x + 6
This is another linear equation with a slope of 3 and a y-intercept of 6. Like the previous equations, it has infinitely many solutions.
System 4: y = -13x - 4
This linear equation has a slope of -13 and a y-intercept of -4. Again, it has infinitely many solutions.
System 5: x - 2y = 6
This equation is linear as well, but it is not in slope-intercept form. To determine the number of solutions, we can rearrange it:
2y = x - 6
y = (1/2)x - 3
This equation has the same form as System 1 and System 3, so it also has infinitely many solutions.
System 6: 3x - 6y = 18
This equation can be rearranged into slope-intercept form:
-6y = -3x + 18
y = (1/2)x - 3
Again, it has the same form as System 1 and System 3, so it has infinitely many solutions.
System 7: y = 23x - 1
This linear equation has a slope of 23 and a y-intercept of -1. Once again, it has infinitely many solutions.
System 8: y = 23x - 2
This equation is similar to System 7; it also has a slope of 23 and a y-intercept of -2. Thus, it has infinitely many solutions.
Based on the above analysis, all of the systems of equations have infinitely many solutions.
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?
To represent the total amount of money Judy will have after saving for d days, we can use the equation:
Total amount of money Judy will have = $100 + ($5 per day) * d
This equation takes into account the initial amount of money Judy has (which is $100) and adds the amount she saves per day, which is $5, multiplied by the number of days she saves, d.
To represent the total amount of money Elenore will have after saving for d days, we can use the equation:
Total amount of money Elenore will have = $75 + ($7 per day) * d
This equation takes into account the initial amount of money Elenore has (which is $75) and adds the amount she saves per day, which is $7, multiplied by the number of days she saves, d.
To find out how many days it will take for Judy and Elenore to have the same amount of money saved, we can set their equations equal to each other and solve for d:
$100 + ($5 per day) * d = $75 + ($7 per day) * d
After finding the value of d, we can substitute it back into either Judy's or Elenore's equation to find out how much money they each have:
Judy's total amount of money = $100 + ($5 per day) * d
Elenore's total amount of money = $75 + ($7 per day) * d
Total amount of money Judy will have = $100 + ($5 per day) * d
This equation takes into account the initial amount of money Judy has (which is $100) and adds the amount she saves per day, which is $5, multiplied by the number of days she saves, d.
To represent the total amount of money Elenore will have after saving for d days, we can use the equation:
Total amount of money Elenore will have = $75 + ($7 per day) * d
This equation takes into account the initial amount of money Elenore has (which is $75) and adds the amount she saves per day, which is $7, multiplied by the number of days she saves, d.
To find out how many days it will take for Judy and Elenore to have the same amount of money saved, we can set their equations equal to each other and solve for d:
$100 + ($5 per day) * d = $75 + ($7 per day) * d
After finding the value of d, we can substitute it back into either Judy's or Elenore's equation to find out how much money they each have:
Judy's total amount of money = $100 + ($5 per day) * d
Elenore's total amount of money = $75 + ($7 per day) * d