Question

The system of equations 2y = 14 - 2x and y=-x+ 7 is

graphed. What is the solution to the system of equations?
yt
14
13
12
(0,-7)
11
10
9
(0,0)
8
7
6
2y = 14 - 2x
y = -x + 7
infinitely many
solutions
5
4
3
2.
1
no solution
0
0 1 2 3 4 5 6 7 8 9 10 11 12 x

Answer 1

• Infinitely many solutions

Explanation:

Given system:

• 2y = 14 - 2x
• y = -x + 7

Divide the first equation by 2 and rearrange:

• 2y/2 = 14/2 - 2x/2
• y = 7 - x
• y = -x + 7

We got the same equation with the second one. It means we have two of the same lines overlapping.

This gives us infinitely many solutions.