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

$x = \frac{19}{13}$
$y = - \frac{5}{13}$

#### Explanation:

start from the given then rearrange
the equations this way

$3 x + y = 4$ first equation
$2 x + 5 y = 1$ second equation

$15 x + 5 y = 20$ after multiplying first equation by 5 -(third equation)

$13 x + 0 = 19$ after subtracting the second from the third equation.

$13 x = 19$ by simplification

divide by 13 now

$\frac{13 x}{13} = \frac{19}{13}$ by simplification

$\frac{\cancel{13} x}{\cancel{13}} = \frac{19}{13}$ by simplification

$x = \frac{19}{13}$

solve $y$ using first equation by substituting the x value.

$3 x + y = 4$ first equation

use $x = \frac{19}{13}$

$3 \left(\frac{19}{13}\right) + y = 4$

$y = 4 - 3 \left(\frac{19}{13}\right)$

$y = \frac{52 - 57}{13}$

$y = - \frac{5}{13}$

have a nice day!!! from the Philippines..