# How do you solve the system of equations algebraically 1/3x-3/2y=-4, 5x-4y=14?

Jan 19, 2017

$y = 4 , x = 6$

#### Explanation:

$\frac{1}{3} x - \frac{3}{2} y = - 4$$\textcolor{w h i t e}{a a}$$- - - - -$(1)
$5 x - 4 y = 14$$\textcolor{w h i t e}{a a a a a}$$- - - - -$(2)
$2 x - 9 y = - 24 \textcolor{w h i t e}{a a a}$$- - - - - \left(1\right) \times 6$--(3)
$10 x - 8 y = 28 \textcolor{w h i t e}{a a a}$$- - - - - \left(2\right) \times 2$--(4)
$10 x - 45 y = - 120 \textcolor{w h i t e}{a a a}$$- - - - - \left(3\right) \times 5$--(5)
$37 y = 148 \textcolor{w h i t e}{a a a}$$- - - - - \left(4\right) - \left(5\right)$
$y = \frac{148}{37}$
$y = 4$
substitute y=4 in (2)

$5 x - 4 \left(4\right) = 14$

$5 x - 16 = 14$

$5 x = 30$

$x = 6$

substitute y=4 and x=6 in (2)

$5 \left(6\right) - 4 \left(4\right) = 14$

$30 - 16 = 14$

$14 = 14$