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Solve using augmented matrices.\newline−7x−7y=14-7x - 7y = 14\newlinex=−8x = -8\newline(_,_)(\_, \_)

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Full solution

Q. Solve using augmented matrices.\newline−7x−7y=14-7x - 7y = 14\newlinex=−8x = -8\newline(_,_)(\_, \_)
  1. Write Augmented Matrix: First, let's write the system of equations as an augmented matrix.\newline[−7−7∣14 10∣−8]\begin{bmatrix} -7 & -7 & | & 14 \ 1 & 0 & | & -8 \end{bmatrix}
  2. Solve Matrix: Now, we need to solve the matrix. Since the second equation is already solved for xx, we can use it to eliminate the xx from the first equation.\newlineMultiply the second row by 77 and add it to the first row.\newline[−7−7∣14]+[7×17×0∣7×−8]=[0−7∣−42]\begin{bmatrix} -7 & -7 | & 14 \end{bmatrix} + \begin{bmatrix} 7\times1 & 7\times0 | & 7\times-8 \end{bmatrix} = \begin{bmatrix} 0 & -7 | & -42 \end{bmatrix}
  3. Solve for yy: Next, divide the first row by −7-7 to solve for yy.0−7∣−42\begin{array}{ccc} 0 & -7 & | & -42 \end{array} / −7-701∣6\begin{array}{ccc} 0 & 1 & | & 6 \end{array} Now we have y=6y = 6.
  4. Find Solution: We already have xx from the second equation, x=−8x = -8. So the solution is (−8,6)(-8, 6).

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