Question

solve the following system of equations.$2x - 5y = -8$$5x - 7y = -20$$x = \square$$y = \square$

Explanation:

Step1: Eliminate x, scale equations

Multiply first equation by 5: $10x - 25y = -40$
Multiply second equation by 2: $10x - 14y = -40$

Step2: Subtract equations to solve y

Subtract scaled eq1 from eq2:
$$(10x - 14y) - (10x - 25y) = -40 - (-40)$$
$$11y = 0$$
$$y = 0$$

Step3: Substitute y=0 into first equation

$$2x - 5(0) = -8$$
$$2x = -8$$

Step4: Solve for x

$$x = \frac{-8}{2} = -4$$

Answer:

$x = -4$
$y = 0$