Question

question
solve the system of equations using elimination: $5x + 4y = 3$ and $4x + 5y = 15$.
answer attempt 1 out of 2

Explanation:

Step1: Eliminate $x$ by scaling 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 $y$

Divide both sides by 9:
$$y = \frac{63}{9} = 7$$

Step4: Substitute $y=7$ into first eq

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

Step5: Solve for $x$

Subtract 28, then divide by 5:
$$5x = 3 - 28 = -25$$
$$x = \frac{-25}{5} = -5$$

Answer:

$x=-5$, $y=7$