# How do you solve the system 4x-5y=-43 , 6x+71=y?

##### 1 Answer
Jun 27, 2017

$x = 12 \mathmr{and} y = 143$

Equate your $y$ value to the first equation.*

Cancel out $5 y$ and find the value of $x$

Substitute the value for $x$ into either of the two equations and solve for $y$

#### Explanation:

Transpose $4 x - 5 y = - 43 \text{ }$ into $\text{ } 5 y = 4 x + 43$
Multiply the second equation, $\text{ "y = 6x + 71" }$ by $\text{ } 5$ to get:

$5 y = 30 x + 355$

*You'll end up with two equations:

$5 y = 4 x + 43$
And
$5 y = 30 x + 355$

Thus,
$4 x + 43 = 30 x + 355$

Transpose your variables and constants and you'll get:

$30 x - 4 x = 355 - 43$

$26 x = 312$

$x = \frac{312}{26}$

$x = 12$

Solve for $y$ since $x = 12 ,$

Use either of the two equations given, I'll use $y = 6 x + 71$

$y = \left(6 x 12\right) + 71$

$y = 143$

$x = 12 \mathmr{and} y = 143$