7.Concept Check Which ordered pair
could be a solution of the graphed sys-
tem of equations? Why?
A.
B.
C.
D.8.Concept Check Which ordered pair
could be a solution of the graphed sys-
tem of equations? Why?
A.
B.
C.
D. 1 0, - 421 0, 4 2
1 - 4, 0 2
1 4, 0 2
1 4, - 42
1 - 4, - 42
1 - 4, 4 2
1 4, 4 2
SECTION 4.1 Systems of Linear Equations in Two Variables 219
The coordinates of their point of intersection are displayed at the bottom of the
screen, indicating that the solution set is. (Compare this graph with the one
in FIGURE 2on page 211.)
For Discussion or Writing
Consider this system.
(1)
(2)Give the slope-intercept form of each equation. Then graph them both in the same
standard viewing window, and give the solution set of the system.
2 x+ 2 y= 8
2 x- 3 y= 3
51 3, 2 26
yx
0yx
0Complete solution available
on the Video Resources on DVD
4.1 EXERCISES
Concept Check Fill in the blanks with the correct responses.
1.If is a solution of a linear system in two variables, then substituting
for xand for yleads to true statements in bothequations.
2.A solution of a system of independent linear equations in two variables is an ordered
.
3.If solving a system leads to a false statement such as the solution set is.
4.If solving a system leads to a true statement such as the system has
equations.
5.If the two lines forming a system have the same slope and different y-intercepts, the
system has solution(s).
(how many?)
6.If the two lines forming a system have different slopes, the system has
solution(s). (how many?)0 =0,
0 =3,
1 4, - 32
9.Concept Check Match each system with the correct graph.
(a)
x-y= 0x+y= 6 (b)
x-y= 0x+y=- 6 (c)
x-y=- 6x+y= 0 (d)
x-y= 6x+y= 0A. B. C. D.
0(3, 3)(^06)
6
y
x^0
x
y y
x
(−3, 3)
(−3, −3)
–6
–6
x
y
(3, −3)
− 6
6
–6 0
6