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

Feb 20, 2017

See the entire solution process below:

#### Explanation:

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

$x + 2 y = 2$

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

$x + 0 = 2 - 2 y$

$x = 2 - 2 y$

Step 2) Substitute $2 - 2 y$ for $x$ in the second equation and solve for $y$:

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

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

$10 - 10 y - 3 y = - 29$

$10 - 13 y = - 29$

$- \textcolor{red}{10} + 10 - 13 y = - \textcolor{red}{10} - 29$

$0 - 13 y = - 39$

$- 13 y = - 39$

$\frac{- 13 y}{\textcolor{red}{- 13}} = - \frac{39}{\textcolor{red}{- 13}}$

$\frac{\textcolor{red}{\cancel{\textcolor{b l a c k}{- 13}}} y}{\cancel{\textcolor{red}{- 13}}} = 3$

$y = 3$

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

$x = 2 - 2 y$ becomes:

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

$x = 2 - 6$

$x = - 4$

The solution is: $x = - 4$ and $y = 3$ or $\left(- 4 , 3\right)$