Question

Solve the systems of equations by elimination
2x+5y = -20
7x + 5y = 5

Answer 1

To solve the system of equations by elimination, we need to eliminate one of the variables by adding or subtracting the equations. In this case, we can eliminate the variable "y" by subtracting the first equation from the second equation.

(7x + 5y) - (2x + 5y) = 5 - (-20)

Simplifying the equation:
7x - 2x + 5y - 5y = 5 + 20

Combine like terms:
5x = 25

Divide both sides by 5:
x = 5

Now, substitute the value of x back into either 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

Therefore, the solution to the system of equations is:
x = 5
y = -6