# Question #4c8a8

Mar 18, 2017

$x = 2 \text{ and } y = 8$

#### Explanation:

We have the following equations.

$x \textcolor{red}{+ y} = 10 \to \left(1\right)$

$\textcolor{red}{y} = 4 x \to \left(2\right)$

Solve using the $\textcolor{b l u e}{\text{substitution method}}$

That is substitute $\textcolor{red}{y} = 4 x \text{ into } \left(1\right)$

$\Rightarrow x + 4 x = 10$

$\Rightarrow 5 x = 10$

divide both sides of the equation by 5

$\frac{\cancel{5} x}{\cancel{5}} = \frac{10}{5}$

$\Rightarrow x = 2$

Substitute this value into ( 2 ) to obtain value for y

$\Rightarrow y = 4 \times 2 = 8$

$\textcolor{b l u e}{\text{As a check}}$

Substitute these values into the original statements and if they are true then these are the solutions.

$x + y = 2 + 8 = 10 \to \text{ True}$

$y = 4 \times 2 = 8 \to \text{ True}$

$\Rightarrow x = 2 \text{ and "y=8" are the solution}$