Question

Four time a number r plus half a number s equals 12. Twice the number r plus one fourth of the numbers s equals 8. What are the two numbers.

Please help

Answer 1

The system of equations have no solution.

Explanation:

The equations are $4r+\frac{1}{2}s=12$ and $2r+\frac{1}{4} s=8$

To find the two numbers, let us solve the equations using substitution method.

From the equation $2r+\frac{1}{4} s=8$, let us determine the value of r,

$\begin{aligned} 2 r+\frac{1}{4} s &=8 \\ 2 r &=8-\frac{1}{4} s \\ r &=\frac{1}{2}\left(8-\frac{1}{4} s\right) \\ r &=4-\frac{1}{8} s \end{aligned}$

Let us substitute the value of r in $4r+\frac{1}{2}s=12$, we get,

$\begin{aligned} 4\left(4-\frac{1}{8} s\right)+\frac{1}{2} s &=12 \\ 16-\frac{1}{2} s+\frac{1}{2} s &=12 \\ 16 &=12 \end{aligned}$

which is not possible.

This means that the system has no solution.