How do solve the following linear system?:  -x+3y=-5 , 2x+7=-5y ?

Mar 19, 2016

I have taken you to a point where you can solve for $x$
$\textcolor{red}{y = - \frac{17}{11}}$

Explanation:

Given:
$- x + 3 y = - 5$ ...............................(1)
$2 x + 7 = - 5 y$.................................(2)

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To solve a single equation you can only do so it contains only one unknown. So to solve any of these two we need to 'get rid of a variable'

Look at equation (1). We have a single $x$. So this is the simpler of the two to use as a source of values for substitution.

$\textcolor{b l u e}{\text{Solving for y}}$

Consider equation (1)

Multiply by (-1) to make the $x$ positive

$x - 3 y = + 5$

Add $3 y$ to both sides

$\textcolor{g r e e n}{x = 3 y + 5} \text{ } \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . \left({1}_{a}\right)$

Substitute for $x$ in equation (2) using equation $\left({1}_{a}\right)$

$\textcolor{b r o w n}{2 x + 7 = - 5 y \text{ "color(blue)(->" } 2 \left(\textcolor{g r e e n}{3 y + 5}\right) + 7 = - 5 y}$

$6 y + 10 + 7 = - 5 y$

$6 y + 5 y = - 17$

$\textcolor{red}{y = - \frac{17}{11}}$ ...................................(3)
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Substitute equation (3) into equation (1) or (2). You chose!

I will let you finish this off.