Question

3/4x - 1/2y =12ax- by = 9The system of equations above has no solutions. If aand b are constants, what is the value of a/b

Answer 1

The given expression is

$\frac{3}{4}x-\frac{1}{2}y=\text{ 12}$$\begin{gathered} \frac{3}{4}x-\frac{1}{2}y=\text{ 12 } \\ \frac{1}{2}y=\frac{3}{4}x-12 \\ y=\frac{3}{2}x-24 \end{gathered}$

the second expression is

$\begin{gathered} ax-by=9 \\ by=ax-9 \\ y=\frac{a}{b}x-\frac{9}{b} \end{gathered}$

for NO solution the coefficient of the x should be equal. that is the slope of the expression

$\frac{a}{b}=\frac{3}{2}$

So the answer is a/b = 3/2 .