Question

$12x + 9y = 43.50$
$8x + 15y = 51.50$

Explanation:

Step1: Eliminate x, scale equations

Multiply first eq by 2: $24x + 18y = 87$
Multiply second eq by 3: $24x + 45y = 154.5$

Step2: Subtract scaled equations

Subtract first scaled eq from second:
$(24x + 45y) - (24x + 18y) = 154.5 - 87$
$27y = 67.5$

Step3: Solve for y

Calculate y: $y = \frac{67.5}{27} = 2.5$

Step4: Substitute y into first equation

Plug $y=2.5$ into $12x + 9y = 43.5$:
$12x + 9(2.5) = 43.5$
$12x + 22.5 = 43.5$

Step5: Solve for x

Isolate x:
$12x = 43.5 - 22.5 = 21$
$x = \frac{21}{12} = 1.75$

Answer:

$x = 1.75$, $y = 2.5$