Match the system with its solution

To match the systems of equations with their solutions, we’ll solve each pair of equations.

1. For the system:

– (y = 3x – 7)

– (y = -2x + 8)

Set them equal to each other:

[

3x – 7 = -2x + 8

]

Solving this gives:

[

3x + 2x = 8 + 7 \

5x = 15 \

x = 3

]

Then substitute (x) back to find (y):

[

y = 3(3) – 7 = 9 – 7 = 2

]

So, the solution is ((3, 2)).

2. For the system:

– (y = 3x + 9)

– (y = -x + 1)

Set them equal:

[

3x + 9 = -x + 1

]

Solving this gives:

[

3x + x = 1 – 9 \

4x = -8 \

x = -2

]

Substitute back to find (y):

[

y = 3(-2) +