Lesson Solving Systems of Equations by Substitution

Finding intersection points by actual graphing has two disadvantages. It is tedious and it is of limited accuracy. In this lesson, you will learn how to calculate such intersection points.
A pair of equations with the same two variables is called a system of equations. The ordered pair where the graphs intersect each other makes both equations true. It is called the solution of the system.

Example 1
To solve the system

you can transform one equation so that a variable is by itself. Solving equation 2 for y in terms of x gives you:

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. So you may substitute

for the y in Equation 1.

The result is an equation with only one variable. Solve it for x.
Distribute the 5

Divide each side by 17

If you want decimal form,

I would use fraction form because it is easier to use.

Substitute your answer for x into the other equation to get your y value.

Now you have your solution:
10/17 and -38/17

If you have attempted to solve by graphing, you would end up with this:

CHECK YOUR ANSWER:
To check, all you need to do is plug the values for x and y into one of the equations. If the statement is true, your answers are correct. If it is false, your answers are incorrect.