# How do you determine the solution in terms of a system of linear equations for 3y = 5x + 15,  6x = 2y - 18 ?

Sep 27, 2015

$x = - 3$
$y = 0$

#### Explanation:

$3 y = 5 x + 15$ ----------------- (1)
6x=2y−18 -----------------(2)

Solve the equation (1) for $y$

$y = \frac{5 x + 15}{3}$

Substitute this in equation (2)

6x=2[(5x+15)/3]−18
6x=[(10x+30)/3]−18 [Multiply both sides by 3

$18 x = 10 x + 30 - 54$
$18 x - 10 x = 30 - 54$
$8 x = - 24$
$x = \frac{- 24}{8} = - 3$

Substitute $x = - 3$ in equation (1)
$3 y = 5 \left(- 3\right) + 15$
$3 y = - 15 + 15$
$3 y = 0$
$y = 0$