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Solve using augmented matrices.\newline−3x+6y=−18-3x + 6y = -18\newlinex=−10x = -10\newline(_,_)(\_, \_)

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Q. Solve using augmented matrices.\newline−3x+6y=−18-3x + 6y = -18\newlinex=−10x = -10\newline(_,_)(\_, \_)
  1. Write Augmented Matrix: First, let's write the system of equations as an augmented matrix.
  2. Eliminate x-term: The system is:\newline−3x+6y=−18-3x + 6y = -18\newlinex=−10x = -10\newlineWe can represent this as:\newline[−36∣−18 10∣−10]\begin{bmatrix} -3 & 6 & | & -18 \ 1 & 0 & | & -10 \end{bmatrix}
  3. Solve for yy: Now, let's use the second equation to eliminate the xx-term in the first equation by adding 33 times the second row to the first row.
  4. Divide by 66: After the row operation, the augmented matrix looks like this:\newline\begin{array}{cc|c} 0 & 6 & -48 \ 1 & 0 & -10 \end{array}
  5. Find xx and yy: Next, we can solve for yy by dividing the first row by 66.
  6. Find xx and yy: Next, we can solve for yy by dividing the first row by 66.Dividing the first row by 66 gives us:\newline\begin{array}{cc|c} 0 & 1 & -8 \ 1 & 0 & -10 \end{array}
  7. Find xx and yy: Next, we can solve for yy by dividing the first row by 66.Dividing the first row by 66 gives us:\newline01∣−8 10∣−10\begin{matrix} 0 & 1 & | & -8 \ 1 & 0 & | & -10 \end{matrix}Now we have the values for xx and yy directly from the matrix:\newlinex=−10x = -10\newliney=−8y = -8

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