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fomenos
3 years ago
5

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
Mathematics
1 answer:
Snezhnost [94]3 years ago
6 0

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.

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