Question

For each ordered pair, determine whether it is a solution to the system of equations.

7x - 4y = 8
y = -9x - 2

(0,-2) is it a solution ?
(5,3) is it a solution ?
(-2,16) is it a solution ?
(-4,-9) is it a solution ?

Answer 1

If the question is asking for a solution for both, then only point (0,2)

Point (0,2) is a solution to both equations

Point (5,3) is a solution to neither (meaning not any of the equations)

Point (-2, 16) is not a solution to the first equation, but is to the second

Point (-4, -9) is a solution to the first, but not to the second.

Explanation:

Using the Property of substitution. 7x-4y=8

(0,-2)

7(0)-4(-2)=8

7(0)=0

-4(-2)=8

0+8=8

This solution is true.

(5,3)

7(5)-4(3)=8

7(5)=35

-4(3)=-12

35-12=23 (not 8)

This solution is not true.

(-2,16)

7(-2)-4(16)=8

-14-64=-78 (not 8)

This solution is not true.

(-4,-9)

7(-4)-4(-9)=8

-28+36=8

This solution is true

__________________________________________________________

Y=-9x-2

(0,-2)

-2=-9(0)-2

-9(0)=0-2=-2

-2=-2

This solution is true

(5,3)

3=-9(5)-2

-45-2=-47

3=-47

This solution is not true

(-2,16)

16=-9(-2)-2

16=18-2

16=16

This solution is true.

(-4,-9)

-9=-9(-4)-2

-9=36-2

-9=34

This solution is not true.