Solve by elimination
x + 2y = -7
x - 5y = 7
To solve the system of equations by elimination, you need to eliminate one variable by adding or subtracting the equations. Here's how you can do it:
Step 1: Multiply one or both of the equations by a constant to make the coefficients of one of the variables in both equations the same or additive inverses.
Let's multiply the second equation by 2 to make the coefficients of x the same:
2(x - 5y) = 2(7) -> 2x - 10y = 14
The system of equations becomes:
x + 2y = -7
2x - 10y = 14
Step 2: Now, we can eliminate x by either adding or subtracting the equations. To eliminate x, multiply the first equation by 2, so the coefficients of x will be additive inverses:
2(x + 2y) = 2(-7) -> 2x + 4y = -14
The system of equations becomes:
2x + 4y = -14
2x - 10y = 14
Step 3: Subtract the equations to eliminate x:
(2x + 4y) - (2x - 10y) = -14 - 14
2x + 4y - 2x + 10y = -28
14y = -28
Divide both sides of the equation by 14: (14y)/14 = -28/14
y = -2
Step 4: Substitute the value of y (which is -2) into either of the original equations to solve for x. Let's use the first equation:
x + 2(-2) = -7
x - 4 = -7
Add 4 to both sides of the equation:
x - 4 + 4 = -7 + 4
x = -3
Hence, the solution to the system of equations is x = -3 and y = -2.
subtract and you have
7y = -14
y = -2
now plug that into either equation to find
x = -3