Question

solve the following system of equations. -0.5x + 1.8y = 4.7 2.5x - 1.9y = 4.9 x = \square y = \square

Explanation:

Step1: Eliminate x, scale first equation

Multiply first equation by 5:
$$5(-0.5x + 1.8y) = 5(4.7)$$
$$-2.5x + 9y = 23.5$$

Step2: Add to second equation

Add scaled equation to the second equation:
$$(-2.5x + 9y) + (2.5x - 1.9y) = 23.5 + 4.9$$
$$7.1y = 28.4$$

Step3: Solve for y

Isolate y by dividing both sides by 7.1:
$$y = \frac{28.4}{7.1} = 4$$

Step4: Substitute y into second equation

Plug $y=4$ into $2.5x - 1.9y = 4.9$:
$$2.5x - 1.9(4) = 4.9$$
$$2.5x - 7.6 = 4.9$$

Step5: Solve for x

Isolate x:
$$2.5x = 4.9 + 7.6 = 12.5$$
$$x = \frac{12.5}{2.5} = 5$$

Answer:

$x = 5$
$y = 4$