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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

User Nehel
by
8.7k points

1 Answer

1 vote

Answer:

  • 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.

User John Kenn
by
8.1k points

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