Solve Systems of Linear Equations: Substitution and Elimination Methods

Published on April 9, 2026

Algebra

Learn to solve systems of linear equations using both substitution and elimination methods. This guide provides step-by-step solutions for two example systems.

Question

Answer

Let’s solve the first system of equations.
The given system of equations is:

We can use the substitution method or the elimination method. Let’s use the elimination method.
Multiply equation (1) by 4 to make the coefficients of

opposites:

Now, add equation (2) and equation (3):

Divide by 63 to solve for

Now substitute the value of

into equation (1):

Add 28 to both sides:

Multiply by -1 to solve for

So, the solution to the first system is

and

Now let’s solve the second system of equations.
The given system of equations is:

We can use the substitution method or the elimination method. Let’s use the elimination method.
Multiply equation (2) by 5 to make the coefficients of

opposites: