Transcript Solution of a System

Solving Linear Systems
by Graphing
Goal:
To solve a system of linear equations by
graphing.
 System
of 2 linear equations
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. This solution will also lie
on the graph of both equations, forming
the intersection point of the two graphs.
Ex: Check whether the ordered pairs (1,
4) and (-5, 0) are solutions of the system:
x  3 y  5
 2 x  3 y  10
(1,4)
Not a solution
1  3(4)  5
1  12  5
 11  5
If the ordered pair
does not work in the
1st solution, there is
no need to check the
2nd solution.
(  5, 0 )
SOLUTION
 5  3(0)  5
 5  5
The ordered pair is a
solution of the 1st ( 5,0)
equation. We must
 2( 5)  3(0)  10
check the 2nd equation
to determine if it is a
10  10
solution to the system
Solving a System
Graphically
1.
2.
3.
4.
Make sure each equation is in slopeintercept form: y = mx + b.
Graph each equation on the same
coordinate plane. (USE GRAPH PAPER!!!)
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 (coincide)– infinitely
many solutions (they have every point in
common).
Ex: Solve the system graphically.
2 x  2 y  8
2x  2 y  4
Solve for ‘y’
y  x4
y  x  2
You can check
(-1, 3) in each
equation to
verify it as a
solution.
Do this on
your paper !!
(-1, 3)
Ex: Solve the system graphically.
x  y  2
2 x  3 y  9
Solve for ‘y’
y  x  2
2
y
x3
3
(-3, 1) is
the
solution.
(-3, 1)