Question

use the elimination method to solve the system equations x+2y=-5 4x+5y=-8

Answer 1

To solve the system of equations using the elimination method, we need to eliminate one variable by multiplying one or both equations by appropriate numbers so that the coefficients of one of the variables will subtract to zero when the equations are added or subtracted.

In this case, let's manipulate the first equation by multiplying it by -4, and the second equation by 1, to make the x-coefficients the same and, therefore, subtract to zero when added together.

Original equations:
1) x + 2y = -5
2) 4x + 5y = -8

Modified equations:
3) -4(x + 2y) = -4(-5) => -4x - 8y = 20
4) 1(4x + 5y) = 1(-8) => 4x + 5y = -8

Now, let's add equations 3 and 4:
(-4x - 8y) + (4x + 5y) = 20 + (-8)
-4x + 4x - 8y + 5y = 12
-3y = 12

Dividing both sides of the equation by -3:
-3y / -3 = 12 / -3
y = -4

Now, substitute the value of y = -4 into one of the original equations (let's use equation 1):
x + 2(-4) = -5
x - 8 = -5
x = -5 + 8
x = 3

Therefore, the solution to the system of equations is x = 3 and y = -4.