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Solve using augmented matrices.\newline4x−6y=−124x - 6y = -12\newliney=−4y = -4\newline(_____, _____)

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Q. Solve using augmented matrices.\newline4x−6y=−124x - 6y = -12\newliney=−4y = -4\newline(_____, _____)
  1. Write Augmented Matrix: First, let's write the system of equations as an augmented matrix.\newlineWe have:\newline4x−6y=−124x - 6y = -12\newliney=−4y = -4\newlineSo the augmented matrix is:\newline\begin{bmatrix}4 & -6 & | & -12\0 & 1 & | & -4\end{bmatrix}
  2. Substitute yy in First Equation: Since the second equation is already solved for yy, we can use it to substitute yy in the first equation.\newlineSubstitute y=−4y = -4 into the first equation:\newline4x−6(−4)=−124x - 6(-4) = -12\newline4x+24=−124x + 24 = -12
  3. Solve for x: Now, let's solve for xx.\newlineSubtract 2424 from both sides:\newline4x=−12−244x = -12 - 24\newline4x=−364x = -36
  4. Find xx: Divide both sides by 44 to find xx:
    x=−364x = \frac{-36}{4}
    x=−9x = -9
  5. Final Solution: We already have yy from the second equation, y=−4y = -4.\newlineSo the solution to the system of equations is:\newlinex=−9x = -9, y=−4y = -4

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