# How do you solve the system 0.5x+4y=-1 and x+2.5y=3.5 using substitution?

Jul 26, 2017

See a solution process below:

#### Explanation:

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

$0.5 x + 4 y = - 1$

$0.5 x + 4 y - \textcolor{red}{4 y} = - 1 - \textcolor{red}{4 y}$

$0.5 x + 0 = - 1 - 4 y$

$\textcolor{red}{2} \times 0.5 x = \textcolor{red}{2} \left(- 1 - 4 y\right)$

$1 x = \left(\textcolor{red}{2} \times - 1\right) - \left(\textcolor{red}{2} \times 4 y\right)$

$x = - 2 - 8 y$

Step 2) Substitute $\left(- 2 - 8 y\right)$ for $x$ in the second equation and solve for $y$:

$x + 2.5 y = 3.5$ becomes:

$\left(- 2 - 8 y\right) + 2.5 y = 3.5$

$- 2 - 8 y + 2.5 y = 3.5$

$\textcolor{red}{2} - 2 - 8 y + 2.5 y = \textcolor{red}{2} + 3.5$

$0 - 8 y + 2.5 y = 5.5$

$- 8 y + 2.5 y = 5.5$

$\left(- 8 + 2.5\right) y = 5.5$

$- 5.5 y = 5.5$

$\frac{- 5.5 y}{\textcolor{red}{- 5.5}} = \frac{5.5}{\textcolor{red}{- 5.5}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 5.5}}} y}{\cancel{\textcolor{red}{- 5.5}}} = - 1$

$y = - 1$

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

$x = - 2 - 8 y$ becomes:

$x = - 2 - \left(8 \cdot - 1\right)$

$x = - 2 - \left(- 8\right)$

$x = - 2 + 8$

$x = 6$

The Solution Is: $x = 6$ and $y = - 1$ or $\left(6 , - 1\right)$