# How do you solve by substitution: 3x-8y=-7 and -5x-6y=3?

May 27, 2018

$y = - \frac{34}{38} \mathmr{and} x = - \frac{269}{57}$

#### Explanation:

$x = \frac{- 7 + 8 y}{3}$

-5(x) - 6y = 3
-5((-7 + 8y)/3) - 6y = 3

(35)/3 + (40y)/3 - 6y = 3
35 + 40y -2y = 1
38y = -34
y = -34/38

x = (-7 + 8(-34/38))/3
x = -269/57

May 27, 2018

$y = + \frac{13}{29}$

I will let you finish off

#### Explanation:

Given:
$+ 3 x - 8 y = - 7 \text{ } \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . E q u a t i o n \left(1\right)$
$- 5 x - 6 y = 3 \text{ } \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . . E q u a t i o n \left(2\right)$

Consider $E q n \left(1\right)$

Add $8 y$ to both sides

$3 x = 8 y - 7$

Divide both sides by 3

$\textcolor{red}{x = \frac{8}{3} y - \frac{7}{3}} \text{ } \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots E q u a t i o n \left({1}_{a}\right)$
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Using $E q n \left({1}_{a}\right)$ substitute for $x$ in $E q n \left(2\right)$

$\textcolor{g r e e n}{- 5 \left(\textcolor{red}{x}\right) - 6 y = 3 \textcolor{w h i t e}{\text{ddd")->color(white)("ddd}} - 5 \left(\textcolor{red}{\frac{8 y}{3} - \frac{7}{3}}\right) - 6 y = 3}$

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{ddddddddddddddd")->color(white)("ddd")-(40y)/3+35/3color(white)("dd}} - 6 y = 3}$

Put everything over 3 to make calculation more straight forward.

$\textcolor{g r e e n}{\textcolor{w h i t e}{\text{ddddddddddddddd")->color(white)("ddd")-(40y)/3+35/3color(white)("dd}} - \frac{18 y}{3} = \frac{9}{3}}$

Multiply both sides by 3

color(green)(color(white)("ddddddddddddddd")->color(white)("ddd")-40y+35color(white)("dd")-18y=9

$- 58 y = - 26$

$y = + \frac{13}{29}$
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I will let you finish off