Solve each system by the substitution method. If a system is inconsistent or has dependent
equations, say so.
258 CHAPTER 4 Systems of Linear Equations
5. 6. 7.
x+ 6 y= 26
9 x-y=- 4
x=
2
3
y
3 x+y=- 4
8. 9. 10.
6 x+ 5 y= 4
3 x+ y= 1
x- 4 y=- 4
2 x- 2 y= 0
5 x+ y= 12
11.
x- y=- 9
1
6
x+
1
6
y=-
1
2
Solve each system of equations by the elimination method. If a system is inconsistent or has
dependent equations, say so.
12.
y= 6 + 3 x
5 x- 4 y= 2
14.Without doing any algebraic work, but answering on the basis of your knowledge of the
graphs of the two lines, explain why the following system has as its solution set.
y= 3 x- 4
y= 3 x+ 2
0
4.2 Solve each system. If a system is inconsistent or has dependent equations, say so.
15.
x+ 2 y+ 2 z=- 3
2 x+ 3 y- z=- 16 16.
x+ 2 z= 7
3 y+ z= 9
4 x- y= 2 17.
4 x+ 2 y+ 3 z= 15
3 x- y- z=- 8
4.3 Solve each problem by using a system of equations.
18.A regulation National Hockey League ice rink has
perimeter 570 ft. The length of the rink is 30 ft longer
than twice the width. What are the dimensions of an
NHL ice rink? (Source:www.nhl.com)
20.A plane flies 560 mi in 1.75 hr traveling with the
wind. The return trip later against the same wind
takes the plane 2 hr. Find the speed of the plane
and the speed of the wind. Let the speed of the
plane and y=the speed of the wind.
x=
rtd
With Wind 1.75
Against Wind 2
x+y
19.In 2009, the New York Yankees and the
Boston Red Sox had the most expen-
sive ticket prices in Major League
Baseball. Two Yankees tickets and three
Red Sox tickets purchased at their aver-
age prices cost $296.66, while three
Yankees tickets and two Red Sox tick-
ets cost $319.39. Find the average
ticket price for a Yankees ticket and a
Red Sox ticket. (Source:Team Market-
ing Report.)
