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Answer:
The solution of the system is:
(x, y) = (-1, -6)
Step-by-step explanation:
Given the system of equations
-6x – 3y = 24
4x – 2y = 8
solving the system of equations
[tex]\begin{bmatrix}-6x-3y=24\\ 4x-2y=8\end{bmatrix}[/tex]
[tex]\mathrm{Multiply\:}-6x-3y=24\mathrm{\:by\:}2\:\mathrm{:}\:\quad \:-12x-6y=48[/tex]
[tex]\mathrm{Multiply\:}4x-2y=8\mathrm{\:by\:}3\:\mathrm{:}\:\quad \:12x-6y=24[/tex]
so
[tex]\begin{bmatrix}-12x-6y=48\\ 12x-6y=24\end{bmatrix}[/tex]
adding the equations
[tex]12x-6y=24[/tex]
[tex]+[/tex]
[tex]\underline{-12x-6y=48}[/tex]
[tex]-12y=72[/tex]
so the system of equations becomes
[tex]\begin{bmatrix}-12x-6y=48\\ -12y=72\end{bmatrix}[/tex]
solve -5y=72 for y
[tex]-12y=72[/tex]
Divide both sides by -12
[tex]\frac{-12y}{-12}=\frac{72}{-12}[/tex]
Simplify
[tex]y=-6[/tex]
[tex]\mathrm{For\:}-12x-6y=48\mathrm{\:plug\:in\:}y=-6[/tex]
solving
[tex]-12x-6\left(-6\right)=48[/tex]
[tex]-12x+6\cdot \:6=48[/tex]
[tex]-12x+36=48[/tex]
subtract 36 from both sides
[tex]-12x+36-36=48-36[/tex]
Simplify
[tex]-12x=12[/tex]
Divide both sides by -12
[tex]\frac{-12x}{-12}=\frac{12}{-12}[/tex]
[tex]x=-1[/tex]
Therefore, the solution of the system is:
(x, y) = (-1, -6)