Transcript Document

Section 7.1
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
Notes-31-Solving a System of
Equations using Graphing
1. Make sure each equation is in slope-intercept
form: y = mx + b.
2. Graph each equation on the same graph paper.
3. The point where the lines intersect is the
solution.
4. Check your solution algebraically.
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)
Classwork
“Two Egg” Worksheet