# How do solve the following linear system?:  3/2x - 3y = -9/4 , 5x+2y=1 ?

Sep 20, 2017

$x = - \frac{1}{12}$

$y = \frac{17}{24}$

#### Explanation:

Multiply through by 2 in the first equation, giving:

$3 x - 6 y = - \frac{9}{2}$

Multiply through by 3 in the second equation, giving:

15x + 6y = 3#

...now add the two equations, which allows you to elimintate the y variable:

$18 x = 3 - \frac{9}{2} = \frac{6}{2} - \frac{9}{2} = - \frac{3}{2}$

$x = - \frac{3}{2 \cdot 18} = - \frac{1}{12}$

...once we know x, we can plug back into either of the initial equations and solve for y:

$5 \left(- \frac{1}{12}\right) + 2 y = 1$
$2 y = 1 + \frac{5}{12} = \frac{17}{12}$

$y = \frac{17}{24}$

SANITY CHECK - we used the second equation to solve for y. Let's plug both our calculated values back into the first equation to double check that the solutions satisfy both equations:

$\frac{3}{2} \left(- \frac{1}{12}\right) - 3 \left(\frac{17}{24}\right) =$

$\frac{- 3 - 51}{24} = - \frac{54}{24} = - \frac{9}{4}$ CHECK!