How to Solve Systems of Equations Using Substitution

An equation is a mathematical expression.

An equation is a mathematical statement that correlates the relationship between two expressions. In a system of equations, two or more equations are correlated. To solve a system of equations, you have to find the values of the variables in the equation. Substitution is one of the simpler ways to solve a system of equations.

Instructions

1. Write both equations on a sheet of paper. Assess both equations to see if a variable is already isolated. For instance, in the equation y = -2x + 9, the y variable is already isolated. If one of your equations does not have an isolated variable, then you have to isolate one variable.

2. Isolate a variable in one of your equations. For instance, if the two equations in your system of equations are 3y - 2x = 11 and y + 2x = 9, you will need to work one equation so that a variable is by itself on one side of the equal sign. By subtracting 2x from each side of y + 2x = 9, you can isolate your y variable. The new equation will read y = -2x + 9.

3. Substitute the equation equal to your isolated variable for the same variable in the second equation. Since you have already established that y = -2x + 9, you can substitute the y in the second equation for -2x +9.

4. Rewrite your new equation. After substituting your isolated variable, your new equation will read 3(-2x + 9) - 2x = 11. Check your new equation to make sure there is only one variable to solve.

5. Solve your new equation for the only variable left. In the equation 3(-2x + 9) - 2x = 11, the value of the x variable is 2. Now you need to find the value of the y variable.

6. Substitute the value of the solved variable into either of the two original equations. In the equation y + 2x = 9, the equation converts to y + 2(2) = 9.

7. Solve for the remaining variable in the converted equation. In y + 2(2) = 9, the value of the y variable is 5. You now have the values of your variables.

8. Check your answers by substituting both variables into one of the original equation. It doesn't matter which equation you choose. In the equation 3y -2x = 11, the equation converts to 3(5) - 2(2) = 11. Simply the equation to make sure it is correct. 15 - 4 = 11 is a correct statement, so you got the right answer.

References

• Purple Math: Systems of Linear Equations: Solving by Substitution
• Regents Prep: Solving Linear Systems
• Syracuse University: Solving Systems of Equations by Substitution
• Spark Notes: Systems of Equations