# How do you solve the following system: y=4x+4, 6x + 7y = -9 ?

May 18, 2018

Well... you already have $y ' s$ value from the first equation but I'm am gonna go ahead and take out $x$ value too

${1}^{s t} \text{ equation}$

color(blue)(y=4x+4

$y - 4 x = 4$

$- 4 x = 4 + y$

color(blue)(x=-(4+y)/4

${2}^{n d} \text{ equation}$

$6 x + 7 y = - 9$

$6 \left(4 x + 4\right) + 6 x = - 9$

Factorize $6$ out of them

$6 \left(\left(4 x + 4\right) + x\right) = - 9$

$4 x + 4 + x = - \frac{9}{6}$

$5 x + 4 = - \frac{3}{2}$

Transfer $4$

$5 x = - \frac{3}{2} - 4$

Make the denominators common

$5 x = - \frac{3}{2} - \frac{8}{2}$

$5 x = - \frac{11}{2}$

Transfer $5$

$x = - \frac{11}{10}$

color(Red)(x=-1.1

$y = 4 x + 4$

$y = 4 \times - \frac{11}{10} + 4$

$y = - \frac{44}{10} + 4$

$y = - 4.4 + 4$

color(red)(y=-0.4