Question

question
solve the system of equations using elimination: $5x + 4y = 3$ and $4x + 5y = 15$
answer attempt 1 out of x
(□,□)

Explanation:

Step1: Eliminate x, scale equations

Multiply first eq by 4: $20x + 16y = 12$
Multiply second eq by 5: $20x + 25y = 75$

Step2: Subtract scaled equations

Subtract first scaled eq from second:
$(20x + 25y) - (20x + 16y) = 75 - 12$
$9y = 63$

Step3: Solve for y

$y = \frac{63}{9} = 7$

Step4: Substitute y into first eq

$5x + 4(7) = 3$
$5x + 28 = 3$

Step5: Solve for x

$5x = 3 - 28 = -25$
$x = \frac{-25}{5} = -5$

Answer:

$(-5, 7)$