 How
do I solve a system of
Linear equations using the
graphing method?

2 equations with 2 variables (x & y) each.
Ax + By = C
Dx + Ey = F

Solution of a System –
an ordered pair, (x,y) that makes both
equations true.
(1,4)
1-3(4)= -5
1-12= -5
-11 = -5
*doesn’t work in the 1st
eqn, no need to check
the 2nd.
Not a solution.
A.
(-5,0)
-5-3(0)= -5
-5 = -5
B.
-2(-5)+3(0)=10
10=10
Solution
1.
2.
3.
Graph each equation on the same
coordinate plane.
If the lines intersect: The point (ordered pair)
where the lines intersect is the solution.
If the lines do not intersect:
a. They are the same line – infinitely many solutions
(they have all points in common).
b. They are parallel lines – no solution
(they have no points in common).
 y  x  2
2
 y x3
3
3
 y  x3
2
3
 y  x3
2
 y x4
 y  x  2
 y  x5
 y  x  5
1.
2.
Define variables
Write as a system of equations
Resort Costs: Resort A charges $70 per night, plus a
one-time surcharge of $5. Resort B charges $65 per
night, plus a one-time surcharge of $20. After how
many nights will the total cost be the same?
x = number of nights
y = total cost
y = 70x + 5
y = 65x + 20
You worked 18 hours last week and earned a
total of $124 before taxes. Your job as a lifeguard
pays $8 per hour, and your job as a cashier pays
$6 per hour. How many hours did you work at
each job?
x = hours as lifeguard
y = hours as cashier
x + y = 18
8x + 6y = 124
A math test is to have 20 questions. The test format
uses multiple choice worth 5 points each and
problem solving worth 6 points each. The test has a
total of 100 points. Write a system to determine how
many of each type of question are used.
x = MC ?’s
y = Problem solving ?’s
x + y = 20
4x + 6y = 100

Finish Homework sheet!