Question

solve the following system of linear equations by addition. indicate whether the given system of linear equations has one solution, has no solution, or has an infinite number of solutions. if the system has one solution, find the solution.$\begin{cases}-6x + 2y = -28 \\2y = 4x - 12end{cases}$answerkeypadkeyboard shortcutsselecting an option will enable input for any required text boxes. if the selected option does not have any associated text boxes, then no further input is required.$circ$ one solution ( $square$ , $square$ )$circ$ no solution$circ$ infinite number of solutions

Explanation:

Step1: Rearrange second equation

$2y - 4x = -12$ or $-4x + 2y = -12$

Step2: Subtract equations

Subtract the rearranged second equation from the first:
$$(-6x + 2y) - (-4x + 2y) = -28 - (-12)$$
$$-6x + 2y + 4x - 2y = -28 + 12$$
$$-2x = -16$$

Step3: Solve for x

$$x = \frac{-16}{-2} = 8$$

Step4: Substitute x into second equation

Substitute $x=8$ into $2y = 4x - 12$:
$$2y = 4(8) - 12$$
$$2y = 32 - 12 = 20$$

Step5: Solve for y

$$y = \frac{20}{2} = 10$$

Answer:

One Solution
$(8, 10)$