Name_______________________________________Date______________Period____
Lesson 5.2
“Solving Systems of Equations: Substitution”
Remember that the solution for a system MUST SATISFY both linear equations!
You learned one method of solving a system of equations, called _________________.
Graphing works nicely when you have whole numbers to work with…
But, there is another method of solving called ________________________________.
The steps to solve a system of equations using SUBSTITUTION, are as follow:
1.
Solve one of the equations for one of the variables
a. This means you need one of the equations to be “y =” or “x =”
2. Substitute the expression from step one, in for the variable that it represents.
a. If step #1 is “y=”, then where you see a “y” in the second equation, you
will replace it with what y is equal to.
3. Solve
4. Finally substitute your solved variable in and solve for the other variable.
Sounds complicated, right? Let us walk through a problem!
Using SUBSTITUTION, find the solution of the following system of equations.
y = -2x – 9
6x – 5y = -19
Since we have a “y = “we will substitute (-2x – 9) for the “y” in the 2nd equation:
6x – 5 (-2x – 9) = -19
We will now simplify the equation by distributing the “-5”:
6x + 10x + 45 = -19
16x + 45 = -19
-45
-45
16x = -64
X = -4
Now substitute “-4” for the x and solve for “y”. I would use the top equation, since it
already says “y = “
y = -2x – 9
y = -2 (-4) – 9
y=8–9
y = -1
(-4, -1) is your final solution for the system
If you were to graph these two linear equations, you would get the same solution 
Let us try another one! What if one of our equations are not already set up as a “y=”
or “x=”?
11x – 7y = -14
x – 2y = -4
so we need to move around one of the equations to get a “y =” or an “x =”. I would
choose “x – 2y = -4”, because it will be easier than the other:
x – 2y = -4
+2y
+2y
x = 2y – 4
so now you will use:
11x – 7y = -14
x = 2y – 4
Substitute “2y – 4” in for the top equation, where you see an “x”:
11 (2y – 4) – 7y = -14
Simplify and solve for “y”:
22y – 44 – 7y = -14
15y – 44 = -14
15y = 30
y=2
plug in y = 2, and solve for “x”:
x = 2y – 4
x = 2 (2) – 4
x=4–4
x=0
The solution to the system is (0, 2)
----------------You try!
6x – 9 = y
5x + 2y = 9
y = -3x
x + y = -3
PRACTICE TIME!! 