3.2 “Solving Linear Systems with Substitution”
Using substitution to solve
systems works best when
there is a “lone” variable.
1. x – 2y = 1
3x + 2y = 19
Steps:
1. Solve for the “lone variable”.
2. Substitute this value into
other equation.
3. Solve that equation for the
variable.
4. Plug in that value into the
“lone variable” equation to
solve for the other value.
5. Write answer as a point (x,y)
More Examples:
2. 3x – 2y = 10
4x + y = 6
3. 4x – 2y = 5
2x = y - 1
Try These:
4. 2x + 5y = 41
2x + y = 13
5. 3y – x = -8
5y + 2x = -6
“Solving Systems Using Elimination”
The Elimination method is AKA
the Addition method. No
limitations using this method.
1. 8x + 3y = 23
4x – 5y = 5
Steps:
1. Get a plan on which
variable to eliminate.
2. Multiply one equation by a
number.
3. Add the two equations and
solve for the variable.
4. Plug in that value into one
of the original equations
and solve for the other
variable.
5. Write answer as a point
(x,y)
More Examples:
2. 3x + 3y = -15
5x – 9y = 3
3. -6x – 5y = 12
3x + 2y = -3
More Examples:
4. 3x - 6y = 9
-4x + 7y = -16
5.
8n = 6m - 3
9m = 12n + 5
More Examples:
6. 3x + 2y = 22
2x – 3y = 6
7. 5x – 7y = 54
2x – 3y = 22
Word Problems 
1. To raise money for new
football uniforms, LDHS sells
T-shirts. The short sleeve
shirts costs the school $8 and
are sold for $11. The long
sleeve shirts costs the school
$10 and sell for $16. The
school spends a total of
$3900 on T-shirts and sells
them for a total of $5925.
How many short and long
sleeve shirts did the school
sell?