Substitute the value ofainto the second equa-
tion and solve for b:
b– (–4) = 1
b+ 4 = 1
b= –3
Since a= –4 and b= –3, the value ofab=
(–4)(–3) = 12.
- b.Solve the second equation for yin terms ofx:
2 x– y= 9
- y= –2x+ 9
y= 2x– 9
Substitute this expression for yin the first
equation and solve for x:
= 8
= 8
x– 3 = 8
x= 11
Substitute the value ofxinto the second equa-
tion and solve for y:
2(11) – y= 9
22 – y= 9
Since x= 11 and y= 13, the value ofx– y=
11 – 13 = –2.
- c.Two lines are parallel if and only if they
have the same slope. The slope-intercept form
of the line x – y= 7 is y= x– 7, and the slope-
intercept form of the line 2 – y= –xis y= x+ 2.
The slope of each of these lines is 1, so, they are
parallel.
331. b.Since the two lines intersect in exactly one
point, we conclude that the system of equa-
tions represented by the graph has one solution.
332. b.The slope-intercept form of the liney – 3x=
–2 is y= 3x– 2. As such, since the slope of this
line, (3) is the same as the slope of the line
given by the first equation, we conclude that
the lines are parallel. Their graphs never inter-
sect, so the system has no solution.
333. b.Solve the first equation for yto obtainy =
3 x– 2. Now, substitute this into the second
equation and solve for x, as follows:
2(3x– 2) – 3x= 8
6 x– 4 – 3x= 8
3 x– 4 = 8
3 x= 12
x= 4
Next, substitute this value ofxinto the first
equation to determine that the corresponding
value ofyisy = 3(4) – 2 = 10. Thus, the value
of^2 yxis ^21 (4 0 )= ^45 .
- c.Since the graph consists of a single line, we
conclude that the two equations that make up
the system are exactly the same, so every point
on the line is a solution of the system. There
are infinitely many such points.
- b.Since the two lines are parallel, they never
intersect. There are no solutions of this system.
- c.Observe that dividing both sides of the sec-
ond equation –3y+ 9x= –6 by –3 and rear-
ranging terms results in the first equation.
This means that the equations are identical, so
any point that satisfies the first equation auto-
matically satisfies the second. Since there are
infinitely many such points, the system has
infinitely many solutions.
^3 x– 9
3
x+ 2x– 9
3
ANSWERS & EXPLANATIONS–
