- e.Solve the second equation for ain terms ofb:
b+ a= 13
a= 13 – b
Substitute this expression for ain the first
equation and solve for b:
–7a+ 4 b= 25
–7(13 – b) + 4 b= 25
7 b– 91 + 4 b= 25
^249 b= 116
29 b= 464
b= 16
- a.Solve the second equation for bin terms ofa:
b+ 2a= –4
b= –2a– 4
Substitute this expression for bin the first
equation and solve for a:
7(2a+ 3(–2a– 4)) = 56
7(2a– 6a – 12) = 56
7(–4a– 12) = 56
–28a– 84 = 56
–28a= 140
a= –5
- b.Solve the second equation for cin terms ofd:
c– 6d= 0
c= 6d
Substitute this expression for cin the first
equation and solve for d:
c– 5 d– 2 = 0
^6 d 5 – d– 2 = 0
^55 d– 2 = 0
d– 2 = 0
d= 2
Substitute the value ofdinto the second equa-
tion and solve for c:
c– 6(2) = 0
c– 12 = 0
c= 12
Since c= 12 and d= 2, the value ofdc= ^122 = 6.
- a.Solve the second equation for yin terms ofx:
- x– y= –6
- y= x– 6
y= –x+ 6
Substitute this expression for yin the first
equation and solve for x:
–5x+ 2(–x+ 6) = –51
–5x– 2x+ 12 = –51
–7x+ 12 = –51
–7x= –63
x= 9
Substitute the value ofxinto the second equa-
tion and solve for y:
–9 – y= –6
Since x= 9 and y= –3, the value ofxy= (9)(–3)
= –27.
- e.Solve the second equation for bin terms ofa:
b– a= 1
b= a+ 1
Substitute this expression for bin the first
equation and solve for a:
10(a+ 1) – 9a= 6
10 a+ 10 – 9a= 6
a+ 10 = 6
a= –4
ANSWERS & EXPLANATIONS–
