We are given a system of two equations: $-7x + 3y = -65$ $-7x + 10y = -135$ We need to find the equation that results from subtracting the second equation from the first equation.

AlgebraLinear EquationsSystems of EquationsEquation ManipulationSubtraction
2025/3/12

1. Problem Description

We are given a system of two equations:
7x+3y=65-7x + 3y = -65
7x+10y=135-7x + 10y = -135
We need to find the equation that results from subtracting the second equation from the first equation.

2. Solution Steps

Let the first equation be (1) and the second equation be (2). We have:
(1) 7x+3y=65-7x + 3y = -65
(2) 7x+10y=135-7x + 10y = -135
We want to compute (1) - (2):
(7x+3y)(7x+10y)=65(135)(-7x + 3y) - (-7x + 10y) = -65 - (-135)
7x+3y+7x10y=65+135-7x + 3y + 7x - 10y = -65 + 135
(7x+7x)+(3y10y)=70(-7x + 7x) + (3y - 10y) = 70
0x7y=700x - 7y = 70
7y=70-7y = 70

3. Final Answer

The equation that results from subtracting the two equations is:
7y=70-7y = 70

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