Match the system with its solution.
y = 3x – 7
y = -2x + 8
y = 3x + 9
y = -x + 1
y = -2x + 4
y = -3x + 7
Match the system with its solution
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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) +