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.

Step-by-step explanation:

The equations are
`4r+(1)/(2)s=12` and
`2r+(1)/(4) s=8`

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

From the equation
`2r+(1)/(4) s=8`, let us determine the value of r,

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

Let us substitute the value of r in
`4r+(1)/(2)s=12`, we get,

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

which is not possible.

This means that the system has no solution.