Name______________________________
Date: _________________ Block: _______
Mrs. Mistron
The solution to a system of linear equation occurs where the two lines intersect. There
are 3 possible scenarios for linear systems:
Exactly One Solution
Infinite Solutions
No Solution
y=x–4
y = 2x – 2
y = 3x + 5
y = 3x + 5
y = 3x + 1
y = 3x + 5
To solve an equation graphically, all we do is graph both equations and find where they
intersect! You must draw your lines carefully using a RULER/STRAIGHTEDGE to get the
correct answer!
Another way to solve systems of linear equations is by SUBSTITUTION. Substitution is
easiest to use when one of the equations is already solved for either x or y
(says x = or y = )
Steps to Solving by Substitution:
Step One Solve one equation for either x or y
Step Two Substitute the expression from step one into the 2nd equation
Step Three Solve the second equation for the given variable
Step Four Plug you solution back into the first equation
Step Five Write your solution as a point.
EXAMPLE ONE Solve by substitution
2x + 5y = – 5
x = – 3y + 3
y = –x – 5
5x – 9y = 3
We can also solve linear systems by the process of elimination. In elimination, we want
the coefficient of one of the variables to be OPPOSITES. This way, when we add the
equations together, it will be eliminated!
Steps to Solving by Elimination:
Step One Multiply one or both equations to make one of the
coefficients be opposite numbers
Step Two Add the two equations together
Step Three Solve for the remaining variable
Step Four Plug in your answer to one of the original equations
Step Five Write you answer as a point
EXAMPLE TWO Solve by Elimination
3x – 7y = 10
6x – 8y = 8
3x – 6y = 9
–4x + 7y = –16
You Try Solve the system by substitution OR elimination
8x + 9y = 15
5x – 2y = 9
EXAMPLE THREE Special Solutions
6x + 15y = –12
–2x – 5y = 9
12x – 3y = –9
–4x + y = 3
EXAMPLE FOUR WORD PROBLEM!
To raise money for the new football uniforms, the school starts selling shirts. Short sleeve
t-shirts cost the school $5.00 and sell for $8.00 while long sleeved t-shirts cost the school
$7.00 and are sold for $12.00. The school spends a total of $2,500 and sells the t-shirts for
$4,200. How many short sleeved t-shirts were sold?
Homework 3.1 # 3 – 13 ODD; 3.2# 31 – 39 ALL, 55, 56, 58, 59