Question

Question 5

The equation which can not be solved in integers is

(a) 5y - 3 = -18

(b) 3x - 9 = 0

(c) 3z + 8 = 3 + z

(d) 9y + 8 = 4y - 7

Answer 1

Let us solve the equations:
(a) Given equation is 5y - 3 = -18
$\Rightarrow 5y=-18+3\Rightarrow 5y=-15\Rightarrow y=-3\left(integer\right)$
(b) Given equation is 3x - 9 = 0
$\Rightarrow 3x=9\Rightarrow x=3\left(integer\right)$
(c) Given equation is 3z + 8 = 3 + z
$\Rightarrow 3z-z=3-8\Rightarrow 2z=-5\Rightarrow z=-\frac{5}{2}$
which is neither a positive fraction nor an integer.
(d) Given equation is 9y + 8 = 4y - 7
$\Rightarrow 9y-4y=-7-85y=-15\Rightarrow \frac{5y}{5}=-\frac{15}{5}\Rightarrow y=-3\left(integer\right)$