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Name: ____________________
Date: ___________
Math 11 Principles
Section 5.1: Solving Systems of Linear Equations by GRAPHING
When you are asked to solve a system of equations, you are being asked to determine all the
ordered pairs (x, y) that satisfy EACH equation in the system.
For example: Is (5, -2) a solution to either of the following systems?
a)
b) x – y = 7
2x + y = 5
x+y=3
x – 2y = 9
In general, the solution to a system of equations (i.e. the ordered pairs) may be determined by
graphing each equation on the same grid. Consider the following examples:
Example 1: A tornado is following a path plotted by the weather office as given by the
equation x – 2y = -8. At the same time, the centre of a thunderstorm is on
the path given by y = 7 – x. At which point might the tornado and
thunderstorm meet?
Graph both linear equations and find the _________________
y=7–x
slope =
x – 2y = -8
slope =
y int =
y int =
Solution  ____________________
Example 2: Solve the following linear system graphically.
4x  y  8
x  2 y  7
Solution  ____________________
Example 3 : Solve the linear system graphically,
then check the result.
(1) 3x  y  11
(2) x  2 y  6
Example 4 : Solve this non-linear system
graphically.
(1) y  x 2
(2) y  x  2
Textbook – page 306 #2, 6ab, 8
and
page 315 #1