# How do you solve 10x – 2y = 8 and 4x – 10y = -6?

May 27, 2017

See a solution process below:

#### Explanation:

Step 1) Solve the first equation for $y$:

$10 x - 2 y = 8$

$\frac{10 x - 2 y}{\textcolor{red}{- 2}} = \frac{8}{\textcolor{red}{- 2}}$

$\frac{10 x}{\textcolor{red}{- 2}} + \frac{- 2 y}{\textcolor{red}{- 2}} = - 4$

$- 5 x + \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 2}}} y}{\cancel{\textcolor{red}{- 2}}} = - 4$

$- 5 x + y = - 4$

$\textcolor{red}{5 x} - 5 x + y = \textcolor{red}{5 x} - 4$

$0 + y = 5 x - 4$

$y = 5 x - 4$

Step 3) Substitute $\left(5 x - 4\right)$ for $y$ in the second equation and solve for $x$:

$4 x - 10 y = - 6$ becomes:

$4 x - 10 \left(5 x - 4\right) = - 6$

$4 x - \left(10 \times 5 x\right) + \left(- 10 \times - 4\right) = - 6$

$4 x - 50 x + 40 = - 6$

$\left(4 - 50\right) x + 40 = - 6$

$- 46 x + 40 = - 6$

$- 46 x + 40 - \textcolor{red}{40} = - 6 - \textcolor{red}{40}$

$- 46 x + 0 = - 46$

$- 46 x = - 46$

$\frac{- 46 x}{\textcolor{red}{- 46}} = \frac{- 46}{\textcolor{red}{- 46}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 46}}} x}{\cancel{\textcolor{red}{- 46}}} = 1$

$x = 1$

Step 3) Substitute $1$ for $x$ in the solution to the first equation at the end of Step 1 and calculate $y$:

$y = 5 x - 4$ becomes:

$y = \left(5 \times 1\right) - 4$

$y = 5 - 4$

$y = 1$

The solution is: $x = 1$ and $y = 1$ or $\left(1 , 1\right)$