Question

solving simultaneous equations using substitution quick check
use the substitution method to solve the system $x = y - 4$, $x + 8y = 2$. (1 point)
$\bigcirc \left(-3\frac{1}{3}, \frac{2}{3}\
ight)$
$\bigcirc$ infinite solutions
$\bigcirc \left(\frac{2}{3}, -3\frac{1}{3}\
ight)$
$\bigcirc$ no solution

Explanation:

Step1: Substitute $x=y-4$ into second equation

$(y-4) + 8y = 2$

Step2: Simplify to solve for $y$

$9y - 4 = 2$
$9y = 6$
$y = \frac{6}{9} = \frac{2}{3}$

Step3: Substitute $y=\frac{2}{3}$ into $x=y-4$

$x = \frac{2}{3} - 4 = \frac{2}{3} - \frac{12}{3} = -\frac{10}{3} = -3\frac{1}{3}$

Answer:

$(-3\frac{1}{3}, \frac{2}{3})$