 Solving Systems of Equations by Substitution Method | Wyzant Resources

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To check, all you need to do is plug the values for x and y into one of the equations. Try to choose the equation where the coefficient of a variable is 1.

Since we have two equations, let's label them as 1 and 2. It is tedious and it is of limited accuracy. In the Substitution Method, we isolate one of the variables in one of the equations and substitute the results in the other equation.

So you may substitute for the y in Equation 1. We usually try to choose the equation where the coefficient of a variable is 1 and isolate that variable.

We choose what variable to express in terms of the other by inspecting the system of equations and guessing which of the two equations looks easier to work with, and which variable will be harder to manipulate.

In some word problems, we may need to translate the sentences into more than one equation. Multiply the whole equation by -1 to get rid of the negative y Where the graphs intersect, the y in one equation stands for the same number as the y in the other.

This will result in an equation with one variable. Step 2 Next, we express one variable in terms of the other variable. Example 2 Solve the following system of equations by substitution Step 1 As in the previous example, it's always good to label you're equations so that you know which one you're working with.

## What does it mean to solve a system of equations by substitution?

Since we have three sets of equations, we need to substitute twice so we need to pick two equations to work with. These algebra lessons introduce the technique of solving systems of equations by substitution. Solving equation 2 for y in terms of x gives you: You can prove this by substituting these values into the original system of equations.

Let's pick equations 2 and 3 Step 3 Take equation 3 and express y in terms of x and z becomes Next we substitute for y in equation 2 becomes.