Question

solve the following system of equations.
7x - 3y = 23
-5x + 2y = -16
x =

y =

Explanation:

Step1: Eliminate y, scale equations

Multiply first eq by 2: $14x - 6y = 46$
Multiply second eq by 3: $-15x + 6y = -48$

Step2: Add scaled equations

$(14x - 6y) + (-15x + 6y) = 46 + (-48)$
$\Rightarrow -x = -2$

Step3: Solve for x

$x = 2$

Step4: Substitute x into first equation

$7(2) - 3y = 23$
$\Rightarrow 14 - 3y = 23$

Step5: Solve for y

$-3y = 23 - 14$
$\Rightarrow -3y = 9$
$\Rightarrow y = -3$

Answer:

$x = 2$
$y = -3$