Find the solution of the system of equations. {:[-8x+12 y=-16],[6x-6y=0]:}

Simplify equation: Simplify the second equation by dividing all terms by 6 to make the coefficients smaller and easier to work with. \[\frac{6x}{6} - \frac{6y}{6} = \frac{0}{6}\] This simplifies to: \[x - y = 0\]Express x in terms of y: Since $x - y = 0$, we can express $x$ in terms of $y$: \[x = y\]Substitute x in first equation: Substitute $x$ with $y$ in the first equation: \[-8(y) + 12y = -16\]Combine like terms: Combine like terms in the equation: \[-8y + 12y = 4y\] So the equation becomes: \[4y = -16\]Solve for y: Solve for $y$ by dividing both sides of the equation by 4: \[\frac{4y}{4} = \frac{-16}{4}\] This gives us: \[y = -4\]Substitute y back into x: Now that we have the value of $y$, we can substitute it back into the equation $x = y$ to find $x$: \[x = -4\]

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Find the solution of the system of equations.

{:[-8x+12 y=-16],[6x-6y=0]:}

Find the solution of the system of equations. $\newline$ $\begin{aligned} -8 x+12 y & =-16 \\ 6 x-6 y & =0 \end{aligned}$

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Q. Find the solution of the system of equations.

\newline

\begin{aligned} -8 x+12 y & =-16 \\ 6 x-6 y & =0 \end{aligned}

Simplify equation: Simplify the second equation by dividing all terms by $6$ to make the coefficients smaller and easier to work with. $\newline$ $\frac{6x}{6} - \frac{6y}{6} = \frac{0}{6}$ $\newline$ This simplifies to: $\newline$ $x - y = 0$
Express x in terms of y: Since $x - y = 0$ , we can express $x$ in terms of $y$ : $\newline$ $x = y$
Substitute x in first equation: Substitute $x$ with $y$ in the first equation: $\newline$ $-8(y) + 12y = -16$
Combine like terms: Combine like terms in the equation: $\newline$ $-8y + 12y = 4y$ $\newline$ So the equation becomes: $\newline$ $4y = -16$
Solve for y: Solve for $y$ by dividing both sides of the equation by $4$ : $\newline$ $\frac{4y}{4} = \frac{-16}{4}$ $\newline$ This gives us: $\newline$ $y = -4$
Substitute y back into x: Now that we have the value of $y$ , we can substitute it back into the equation $x = y$ to find $x$ : $\newline$ $x = -4$