Question

Solve the below system of equations using the linear combination method.   Show all your work, explaining each step in solving the system using the linear combination method.

2x + 3y = 1

y = -2x - 9

Answer 1

The solution to given system of equations is x = -7 and y = 5

Solution:

Given that, we have to solve the system of equations by linear combination method

Given system of equations are:

2x + 3y = 1 ---------- eqn 1

y = -2x - 9 ----------- eqn 2

We can use substitution method to solve the system of equations

Substitute eqn 2 in eqn 1

2x + 3(-2x - 9) = 1

Add the terms inside the bracket with constant outside the bracket

2x -6x - 27 = 1

Combine the like terms

-4x = 1 + 27

-4x = 28

Divide both sides of equation by -4

x = -7

Substitute x = -7 in eqn 2

y = -2(-7) - 9

Simplify the above equation

y = 14 - 9

y = 5

Thus solution to given system of equations is x = -7 and y = 5