Solve the systems of equations by elimination
2x+5y = -20
7x + 5y = 5
To solve this system of equations by elimination, we want to eliminate one of the variables by adding or subtracting the two equations. In this case, notice that if we subtract the first equation from the second equation, we can eliminate the y variable:
(7x + 5y) - (2x + 5y) = 5 - (-20)
7x - 2x + 5y - 5y = 5 + 20
5x + 0 = 25
5x = 25
x = 25/5
x = 5
Now that we have the value of x, we can substitute it back into one of the original equations to solve for y. Let's use the first equation:
2x + 5y = -20
2(5) + 5y = -20
10 + 5y = -20
5y = -20 - 10
5y = -30
y = -30/5
y = -6
So the solution to the system of equations is x = 5 and y = -6.