# How do you solve the following linear system: 8y-24= -6x, color(white)("ddd")3x+4y=12?

##### 1 Answer
Jun 10, 2018

There is an infinite count of solutions.

#### Explanation:

Given:

$8 y - 24 = - 6 x \text{ } \ldots \ldots \ldots \ldots \ldots \ldots \ldots E q u a t i o n \left(1\right)$
$3 x + 4 y = 12 \text{ } \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots . E q u a t i o n \left(1\right)$

Consider $E q u a t i o n \left(1\right)$

Divide all of both sides by 2 giving:

$4 y - 12 = - 3 x \text{ } \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots \ldots E q u a t i o n \left({1}_{a}\right)$

With a bit of manipulation of $E q n \left({1}_{a}\right)$ you will realise that it the same as $E q n \left(2\right)$

Thus the plot of one is superimposed onto the plot of the other.

Thus there is an infinite count of shared points.

Thus the is an infinite count of solutions.