Question

use the linear combination method to solve the system of equations. Explain each step of your solution. 2x-3y=13 x+2y=-4

Answer 1

Solution: x = 2, y = -3.

Explanation:

Given system of equations:

Equation 1: 2x - 3y = 13

Equation 2: x + 2y = -4

Multiply Equation 2 by 2:

2(x + 2y) = 2(-4)

Simplified: 2x + 4y = -8

Add Equation 1 and Equation 3:

4x + y = 5

Solve Equation 4 for y:

y = 5 - 4x

Substitute y into Equation 2:

x + 2(5 - 4x) = -4

Simplify:

-7x + 10 = -4

Solve for x:

x = 2

Substitute x into Equation 5:

y = 5 - 4(2)

y = -3

Solution: x = 2, y = -3.