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## Algebra 1 – Solve a system of equations using substitution

## Algebra 1 - Solve a system of equations using substitution | Lumos Learning

### SOLVING SYSTEMS OF EQUATIONS BY SUBSTITUTION

In this section, we will define a completely algebraic technique for solving systems. The idea is to solve one equation for one of the variables and substitute the result into the other equation. After performing this substitution step, we will be left with a single equation with one variable, which can be solved using algebra. This is called the substitution method, and the steps are outlined in the following example. Step 1 : Solve for either variable in either equation.

The substitution method is most useful for systems of 2 equations in 2 unknowns. The main idea here is that we solve one of the equations for one of the unknowns, and then substitute the result into the other equation. We will solve second equation for y. Note: It does not matter which equation we choose first and which second. Just choose the most convenient one first! Since the coefficient of y in equation 2 is -1, it is easiest to solve for y in equation 2. Do not worry about your difficulties in mathematics, I assure you that mine are greater.

Alissa is currently a teacher in the San Francisco Bay Area and Brightstorm users love her clear, concise explanations of tough concepts. To unlock all 5, videos, start your free trial. A system of equations is two or more equations that contain the same variables. Solving systems of equations by substitution is one method to find the point that is a solution to both or all original equations. Besides solving systems of equations by substitution, other methods of finding the solution to systems of equations include graphing , elimination and matrices.

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