Question

solve the following system using the substitution method.
$2x + 4y = -3$
$9x - 5y = 16.4$

Explanation:

Step1: Isolate x from first equation

$2x = -3 - 4y$
$x = \frac{-3 - 4y}{2} = -1.5 - 2y$

Step2: Substitute x into second equation

$9(-1.5 - 2y) - 5y = 16.4$
$-13.5 - 18y - 5y = 16.4$
$-13.5 - 23y = 16.4$

Step3: Solve for y

$-23y = 16.4 + 13.5$
$-23y = 29.9$
$y = \frac{29.9}{-23} = -1.3$

Step4: Substitute y back to find x

$x = -1.5 - 2(-1.3)$
$x = -1.5 + 2.6$
$x = 1.1$

Answer:

$x = 1.1$, $y = -1.3$