Question

solve the system of equations.
$-2x + 5y = 13$
$16x + 3y = 25$
$x = square$
$y = square$
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Explanation:

Step1: Eliminate x, scale first eq

Multiply first equation by 8:
$$8(-2x + 5y) = 8 \times 13$$
$$-16x + 40y = 104$$

Step2: Add to second equation

Add scaled eq to second eq:
$$(-16x + 40y) + (16x + 3y) = 104 + 25$$
$$43y = 129$$

Step3: Solve for y

Divide both sides by 43:
$$y = \frac{129}{43} = 3$$

Step4: Substitute y into first eq

Plug $y=3$ into $-2x + 5y = 13$:
$$-2x + 5(3) = 13$$
$$-2x + 15 = 13$$

Step5: Solve for x

Isolate x:
$$-2x = 13 - 15 = -2$$
$$x = \frac{-2}{-2} = 1$$

Answer:

$x = 1$
$y = 3$