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Solve using augmented matrices.\newlinex=−8x = -8\newline−9x−10y=−18-9x - 10y = -18\newline(_____, _____)

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Full solution

Q. Solve using augmented matrices.\newlinex=−8x = -8\newline−9x−10y=−18-9x - 10y = -18\newline(_____, _____)
  1. Write Equations in Standard Form: First, let's write the system of equations in standard form. \newlinex=−8x = -8 becomes 1x+0y=−81x + 0y = -8\newline−9x−10y=−18-9x - 10y = -18 stays the same.
  2. Create Augmented Matrix: Now, let's create the augmented matrix for the system.\newline[10∣−8 −9−10∣−18]\begin{bmatrix} 1 & 0 & \vert & -8 \ -9 & -10 & \vert & -18 \end{bmatrix}
  3. Substitute and Solve for xx: We already have the value of xx, which is –8–8. So, we just need to use the second equation to find yy.\newlineSubstitute x=–8x = –8 into –9x−10y=–18–9x − 10y = –18.\newline–9(–8)−10y=–18–9(–8) − 10y = –18\newline72−10y=–1872 − 10y = –18
  4. Solve for y: Now, let's solve for y.\newline72−10y=−1872 - 10y = -18\newline−10y=−18−72-10y = -18 - 72\newline−10y=−90-10y = -90\newliney=−90−10y = \frac{-90}{-10}\newliney=9y = 9

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