Page 43 - Algebra
P. 43
2y = 6
y = 3 years
4x – 3(3) = 6 4x = 15
x = 3.75 years
7. Parallel lines from the graph indicate that the system of equations has no solution. So,a1 =b1 ≠c1
a2 b2 c2
a1 = 4, b1 =5, c1 = – p
a2 = –8, b2 =–10, c2 = – q
4 = 5 ≠−p −8 −10 −q
p −1 In all the options except for (e), q is 2 .
p −4 −2 In option (e), q is 6 or 3 .
It satisfies (1).
3
8. 5x–y–12=0
6x – 10y – 24 = 0
a1 = 3, b1 =–1, c1 = – 12
5
a2 = 6, b2 =–10, c2 = –24
a1 = 3 ÷ 6 = 1
b1 = 1 b2 10
−1 −1 p 2 = 2 ≠ q
....... (1)
Go by the elimination method from the choices.
a2 5 10
c1 −12 1
==
c2 −24 2
So,
a1 =b1 ≠c1 a2 b2 c2
1=1=1
10 10 2
It means that the system of equation has no solution.
9. The easiest way to solve the problem is by finding the ratios of the coefficients. 1syste2x + 11y – 6 = 0
11 3
3x + 𝑦 – = 0
a1 =12, b1 = 11, c1 = –6
42
a2 = 3, b2 = , c2 = –
42 a1 = 12 = 4
a2 3
11 3
Page 42 of 177
Algebra I & II
