Systems of Equations for Kids: Solve Two Equations by Graphing and Substitution (Grade 8 Math)

Hi, I'm Luna from DoodleBeez. Today we are solving systems of equations. A system is two equations with the same two unknowns. The solution is the pair of numbers that makes both equations true at once.

Each equation makes a straight line on a graph. The solution is the point where the two lines cross, because that point sits on both lines. Here the lines cross at the point four, eight.

We can also solve with algebra. Take x plus y equals ten and x minus y equals two. Add the equations, and the y terms cancel. Two x equals twelve, so x is six. Then six plus y is ten, so y is four.

Another method is substitution. If y equals two x, and x plus y equals twelve, swap two x in for y. Then x plus two x equals twelve, so three x is twelve and x is four. Then y is eight.

Check the answer in both equations. Is eight equal to two times four? Yes. Is four plus eight equal to twelve? Yes. That is why the lines on our graph crossed at four, eight.

Not every system has one answer. If the two lines are parallel, they never cross, so there is no solution. If both equations make the very same line, every point works, so there are infinitely many solutions.

Now it's your turn. Solve the system y equals two x and x plus y equals nine. Pause and try. Substitute to get three x equals nine, so x is three. Then y is six.

Great job! Remember, the solution to a system makes both equations true, it is where the lines cross, and you can find it by adding the equations or substitution. Practice systems of equations in Middle School Math at doodlebeez.com. See you next time!