How to Solve Systems of Equations
In this lesson you will learn how to solve systems of equations.
Graphing Method
2x – y =  9
x + y = 6
The graph of the first equation is the red line, and the graph of the second equation is the blue line. The xcoordinate of the point of intersection between the two graphs is x = 1 and the ycoordinate is y = 7. Therefore the solution of our system is x=  1, y = 7.
Substitution Method
This method consists in expressing one variable in terms of the other one. In the second equation, x + y = 6, we can isolate x by subtracting y from both sides of the equation.
We get x = 6 – y
Replace x with 6  y in the first equation.
2(6  y) – y =  9
Apply the distributive property.
12 – 2y –y =  9
Combine the like terms.
12 – 3y =  9
3y =  21
Divide by  3 on both sides.
y = 7
To find x, return to x = 6 – y and replace y with y.
x = 6 – 7 =  1
Elimination Method
2x – y =  9
x + y = 6
Add the two equations to eliminate y.
(2x + x) + ( y +y) =  9 + 6
3x + 0 = 3
3x =  3
x =  1
To find y replace x with 1 in the second equation.
1 + y = 6
y = 7
Return from the
Systems of Equations
page to
Algebra Videos
or to
8th Grade CRCT Math.
