Question

solve the system of equations. state the decimal solution to the nearest hundredth.
$3.5x + 4.2y = 8.6$
$7.5x - 2y = -2.2$
approximately ( , )
need help?

Explanation:

Step1: Eliminate x via scaling equations

Multiply first eq by 7.5, second by 3.5:
$$7.5(3.5x + 4.2y) = 7.5(8.6) \implies 26.25x + 31.5y = 64.5$$
$$3.5(7.5x - 2y) = 3.5(-2.2) \implies 26.25x - 7y = -7.7$$

Step2: Subtract equations to solve for y

Subtract second new eq from first:
$$(26.25x + 31.5y) - (26.25x - 7y) = 64.5 - (-7.7)$$
$$38.5y = 72.2$$
$$y = \frac{72.2}{38.5} \approx 1.8753 \approx 1.88$$

Step3: Substitute y to solve for x

Plug $y \approx 1.88$ into $3.5x + 4.2y = 8.6$:
$$3.5x + 4.2(1.88) = 8.6$$
$$3.5x + 7.896 = 8.6$$
$$3.5x = 8.6 - 7.896 = 0.704$$
$$x = \frac{0.704}{3.5} \approx 0.2011 \approx 0.20$$

Answer:

$(0.20, 1.88)$