SECTION 4.1 Solving Systems of Linear Equations by Graphing^253
We can solve the system from Example 1(a)by graphing with a calculator.
To enter the equations in a graphing calculator, first solve each equation for y.
Subtract x. Subtract 3x.Divide by 4. Divide by 2.We designate the first equation and the second equation See FIGURE 6(a). We
graph the two equations using a standard window and then use the capability of
the calculator to find the coordinates of the point of intersection of the graphs. See
FIGURE 6(b).For Discussion or Writing
Use a graphing calculator to solve each system.
Y 1 Y 2.
y=-
3
2
y=- x+ 3
1
4
x- 2
4 y=-x- 8 2 y=- 3 x+ 6
x+ 4 y=- 8 3 x+ 2 y= 6
3 x+ 2 y= 6
x+ 4 y=- 8
CONNECTIONS
10–10–10^10
(a)1. 2. 3.
4 x+ 2 y= 3
3 x+ 3 y= 0
4 x- 2 y= 2
8 x+ 4 y= 0
2 x-y=- 7
3 x+ y= 2
(b)
FIGURE 6The display at the bottom of the
screen indicates that the solution
set is 51 4, - 326.
Complete solution available
on the Video Resources on DVD
4.1 EXERCISES
Decide whether the given ordered pair is a solution of the given system. See Example 1.1.Concept Check Which ordered pair
could not be a solution of the system
graphed? Why is it the only valid
choice?
A. B.
C. D.2.Concept Check Which ordered pair
could be a solution of the system
graphed? Why is it the only valid
choice?
A. B.
C. 1 - 2, 0 2 D. 1 0, - 221 2, 0 2 1 0, 2 2
1 - 4, 4 2 1 - 3, 3 2
1 - 4, - 42 1 - 2, 2 2
y0 xyx
03. 4. 5.
4 x+ 2 y=- 103 x+ 5 y=- 181 - 1, - 32
3 x+ 5 y= 3x+ 2 y= 101 4, 3 2
2 x+ 5 y= 19x+ y=- 11 2, - 32
6. 7. 8.
3 x= 24 + 3 y2 x= 23 - 5 y1 9, 1 2
3 x= 29 + 4 y4 x= 26 - y1 7, - 22
3 x+ 6 y=- 392 x- 5 y=- 81 - 9, - 22
Notice the careful
use of parentheses
with the fractions.