Answered

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Solve the system and write your answer as a coordinate point. I
(1 Point)
-6x – 3y = 24
4x – 2y = 8

Sagot :

absor201

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)

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