Question

Which system of linear equations has the ordered pair (-2,8) as its solution?

Answer 1

Answer:

The solution to the system of linear equations is:

(x, y) = (-2, 8)

Hence, y - 2x = 12 and x - 2y = -18  has the ordered pair (-2,8) as its solution. Thus, option A is correct.

Step-by-step explanation:

Checking the first system of equations

y - 2x = 12

x - 2y = -18

solving the first system of equations

$\begin{bmatrix}y-2x=12\\ x-2y=-18\end{bmatrix}$

$\mathrm{Multiply\:}y-2x=12\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:2y-4x=24$

$\begin{bmatrix}2y-4x=24\\ -2y+x=-18\end{bmatrix}$

adding the equations

$-2y+x=-18$

$+$

$\underline{2y-4x=24}$

$-3x=6$

$\begin{bmatrix}2y-4x=24\\ -3x=6\end{bmatrix}$

solving -3x=6 for x

$-3x=6$

Divide both sides by -3

$\frac{-3x}{-3}=\frac{6}{-3}$

Simplify

$x=-2$

$\mathrm{For\:}2y-4x=24\mathrm{\:plug\:in\:}x=-2$

$2y-4\left(-2\right)=24$

$2y+8=24$

Subtract 8 from both sides

$2y+8-8=24-8$

Simplify

$2y=16$

Divide both sides by 2

$\frac{2y}{2}=\frac{16}{2}$

Simplify

$y=8$

Therefore, the solution to the system of linear equations is:

(x, y) = (-2, 8)

Hence, y - 2x = 12 and x - 2y = -18  has the ordered pair (-2,8) as its solution. Thus, option A is correct.