# How do you solve 0.05x+0.25y=66 and 0.15x+0.05y=72 using substitution?

Aug 26, 2017

See a solution process below: $\left(420 , 180\right)$

#### Explanation:

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

$0.05 x + 0.25 y = 66$

$- \textcolor{red}{0.05 x} + 0.05 x + 0.25 y = - \textcolor{red}{0.05 x} + 66$

$0 + 0.25 y = - 0.05 x + 66$

$0.25 y = - 0.05 x + 66$

$\textcolor{red}{4} \times 0.25 y = \textcolor{red}{4} \left(- 0.05 x + 66\right)$

$1 y = \left(\textcolor{red}{4} \times - 0.05 x\right) + \left(\textcolor{red}{4} \times 66\right)$

$y = - 0.2 x + 264$

Step 2) Substitute $\left(- 0.2 x + 264\right)$ for $y$ in the second equation and solve for $x$:

$0.15 x + 0.05 y = 72$ becomes:

$0.15 x + 0.05 \left(- 0.2 x + 264\right) = 72$

$0.15 x + \left(0.05 \times - 0.2 x\right) + \left(0.05 \times 264\right) = 72$

$0.15 x + \left(- 0.01 x\right) + 13.2 = 72$

$0.15 x - 0.01 x + 13.2 = 72$

$\left(0.15 - 0.01\right) x + 13.2 = 72$

$0.14 x + 13.2 = 72$

$0.14 x + 13.2 - \textcolor{red}{13.2} = 72 - \textcolor{red}{13.2}$

$0.14 x + 0 = 58.8$

$0.14 x = 58.8$

$\frac{0.14 x}{\textcolor{red}{0.14}} = \frac{58.8}{\textcolor{red}{0.14}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{0.14}}} x}{\cancel{\textcolor{red}{0.14}}} = 420$

$x = 420$

Step 3) Substitute $420$ for $x$ in the solution to the first equation at the end of Step 1 and calculate $y$:

$y = - 0.2 x + 264$ becomes:

$y = \left(- 0.2 \times 420\right) + 264$

$y = - 84 + 264$

$y = 180$

The Solution Is: $x = 420$ and $y = 180$ or $\left(420 , 180\right)$