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

Mar 17, 2017

See the entire solution process below:

#### Explanation:

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

$x - 2 y = - 3$

$x - 2 y + \textcolor{red}{2 y} = - 3 + \textcolor{red}{2 y}$

$x - 0 = - 3 + 2 y$

$x = - 3 + 2 y$

Step 2) Substitute $- 3 + 2 y$ for $x$ in the second equation and solve for $y$:

$2 x - 5 y = 3$ becomes:

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

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

$- 6 + 4 y - 5 y = 3$

$- 6 + \left(4 - 5\right) y = 3$

$- 6 - y = 3$

$\textcolor{red}{6} - 6 - y = \textcolor{red}{6} + 3$

$0 - y = 9$

$- y = 9$

$\textcolor{red}{- 1} \times - y = \textcolor{red}{- 1} \times 9$

$y = - 9$

Step 3) Substitute $- 9$ for $y$ in the solution to the first equation at the end of Step 1 and calculate $x$:

$x = - 3 + 2 y$ becomes:

$x = - 3 + \left(2 \times - 9\right)$

$x = - 3 - 18$

$x = - 21$

The solution is: $x = - 21$ and $y = - 9$ or $\left(- 21 , - 9\right)$