# How do solve the following linear system?:  4x+3y=1 , 11x + 3y + 7 = 0 ?

May 5, 2017

$x = - \frac{8}{7} = - 1 \frac{1}{7}$

$y = \frac{13}{7} = 1 \frac{6}{7}$

#### Explanation:

Given: $4 x + 3 y = 1$; $11 x + 3 y + 7 = 0$

From $4 x + 3 y = 1$ we can subtract $4 x$ from both sides

to get $3 y = 1 - 4 x$ which we can substitute into the other

equation for $3 y$:

$11 x + 3 y + 7 = 0$

$11 x + 1 - 4 x + 7 = 0$

$11 x + 1 - 4 x + 7 = 0$

$7 x = - 8$

$x = - \frac{8}{7}$ answer x

Substitute value for $x$ into $4 x + 3 y = 1$ to find $y$:

$4 \left(- \frac{8}{7}\right) + 3 y = 1$

$3 y = 1 + \frac{32}{7}$

$3 y = \frac{39}{7}$

$y = \frac{13}{7}$ answer y

To check, substitute into the $g i v e n$ equation:

$11 x + 3 y + 7 = 0$

$11 \left(- \frac{8}{7}\right) + 3 \left(\frac{13}{7}\right) + 7 = 0$

$\left(- \frac{88}{7}\right) + \left(\frac{39}{7}\right) + \left(\frac{49}{7}\right) = 0$

$\left(- 88\right) + \left(39\right) + \left(49\right) = 0$

$- 88 + 88 = 0$