NAME
DATE
9 Systems of Linear Equations
9-1 The Graphing Method
Objective: To use graphs to solve
systems of linear equations.
Vocabulary
system of equations Two or more equations in the same variables. AIso
called a system of simultaneous equations.
To solve a system of equations To find ail ordered pairs (r, y) that make
both equations true.
solution of a system of equations An ordered pair that sdtisfies both
equations at the same time.
coincide Two lines coincide if their graphs are the same. The equations
are equivalent.
Example
1
Solve the system by graphing:
2x-y-L
x*Y=J
Solution
Graph2x-y = landx+y =5inthe
same coordinate plane. The only point
on both lines is the intersection point
(2,3).The only solution of both
)
equations is (2, 3).
Check: You can check that (2,3) is a
solution of the system by substituting
x = 2 and y 3 in both equations.
o
:
b-y:l
2(2)-3:1
W
x*y=J
2*3=5
+r
The system has the solution (2,3).
Solve each system by the graphing method.
l.x*!:6
x-l:2
4'Y:x*2
Y:2x-I
7.2x * y:5
x-y:4
10.-Zx*y:-1
2x+Y=7
2.x*)=5
x-y--3
5.2,x-):0
x*y-3
8. x * 2y:5
x-Y=-l
11.y-2x=-5
y-x=-J
Study Guide, ALGEBRA, Structure and Method, Book 1
Copyright @ by Houghton Mifftin Company. All rights reserved.
x*y-9
x-y:3
6. 2x+y:1
x*y-3
9. x-Y=4
2x*y:2
t2. 2y-x:2
Y*x:4
3.
153
DATE
NAME
The GraPhing Method
(continued)
Solve the system by
graphingt
:-_'lr::O-,
When you graph the equations in the same
have
coordinate plane, you see that the lines
The
the same slope but different y-intercepts'
do
graphs are parallel lines' Since the lines
represents
that
point
no
iot intersect, there is
tl| | ,4v
v
-
4+
o
ltl
a solution ofboth equations'
The svstem has no solution'
Solve the system by
graphing: x * y -= 3
2x*2Y=
When you graph the equations in the same
graphs
coordinate plun., you see that the
coincide. The equations are equivalent'
Every point on ih" lint represents a solution
of both equations'
tt
?_l
\ ).T
o
l
I\R{'
+
The systern has infinitely mnny solutions'
i
i
\
lilir
i,l
i1
method'
Solve each system by the graphing
] =8
x*y:4
16.3x + 3Y :9
xly:3
19.x-Y:-6
x-y--2
22.2x-!=7
x*2Y=lt
13,3x -
14.2x*3Y=5
y.= x
17. x * 2Y : -4
x*2Y=$
20.Y-x:-3
y-Zx- -J
23'4x*Y=-t4
3x=!
15,2x-3Y=4
b-y:o
18.3.x*Y:6
2x - Y: -l
21.2x*Y:5
2xtY--1
24. x - !:4
2x-2y:g
Mixed Review Exercises
positive exponents'
Simptify. Give your answers using
.,
l6a2b
z.
@-2a3f
s.
xay-3
3.
8ab'
4. 6zrz1-z
6.
s
l)m'n
,5#"3
x-Y
,r,
t'lt
I r.-^L^J
O-^1.
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