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
[tex]\begin{bmatrix}y-2x=12\\ x-2y=-18\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}y-2x=12\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:2y-4x=24[/tex]
[tex]\begin{bmatrix}2y-4x=24\\ -2y+x=-18\end{bmatrix}[/tex]
adding the equations
[tex]-2y+x=-18[/tex]
[tex]+[/tex]
[tex]\underline{2y-4x=24}[/tex]
[tex]-3x=6[/tex]
[tex]\begin{bmatrix}2y-4x=24\\ -3x=6\end{bmatrix}[/tex]
solving -3x=6 for x
[tex]-3x=6[/tex]
Divide both sides by -3
[tex]\frac{-3x}{-3}=\frac{6}{-3}[/tex]
Simplify
[tex]x=-2[/tex]
[tex]\mathrm{For\:}2y-4x=24\mathrm{\:plug\:in\:}x=-2[/tex]
[tex]2y-4\left(-2\right)=24[/tex]
[tex]2y+8=24[/tex]
Subtract 8 from both sides
[tex]2y+8-8=24-8[/tex]
Simplify
[tex]2y=16[/tex]
Divide both sides by 2
[tex]\frac{2y}{2}=\frac{16}{2}[/tex]
Simplify
[tex]y=8[/tex]
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.
