# How do you solve the following system: 2x+y=5, -29=5y-3x ?

Jul 27, 2017

See a solution process below:

#### Explanation:

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

$2 x + y = 5$

$- \textcolor{red}{2 x} + 2 x + y = - \textcolor{red}{2 x} + 5$

$0 + y = - 2 x + 5$

$y = - 2 x + 5$

Step 2) Substitute $\left(- 2 x + 5\right)$ for $y$ in the second equation and solve for $x$:

$- 29 = 5 y - 3 x$ becomes:

$- 29 = 5 \left(- 2 x + 5\right) - 3 x$

$- 29 = \left(5 \times - 2 x\right) + \left(5 \times 5\right) - 3 x$

$- 29 = - 10 x + 25 - 3 x$

$- 29 = - 10 x - 3 x + 25$

$- 29 = \left(- 10 - 3\right) x + 25$

$- 29 = - 13 x + 25$

$- 29 - \textcolor{red}{25} = - 13 x + 25 - \textcolor{red}{25}$

$- 54 = - 13 x + 0$

$- 54 = - 13 x$

$\frac{- 54}{\textcolor{red}{- 13}} = \frac{- 13 x}{\textcolor{red}{- 13}}$

$\frac{54}{13} = \frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 13}}} x}{\cancel{\textcolor{red}{- 13}}}$

$\frac{54}{13} = x$

$x = \frac{54}{13}$

Step 3) Substitute $\frac{54}{13}$ for $x$ in the solution to the first equation at the end of Step 1 and calculate $y$:

$y = - 2 x + 5$ becomes:

$y = \left(- 2 \times \frac{54}{13}\right) + 5$

$y = - \frac{108}{13} + 5$

$y = - \frac{108}{13} + \left(\frac{13}{13} \times 5\right)$

$y = - \frac{108}{13} + \frac{65}{13}$

$y = - \frac{43}{13}$

The Solution Is: $x = \frac{54}{13}$ and $y = - \frac{43}{13}$ or $\left(\frac{54}{13} , - \frac{43}{13}\right)$