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23x−43y=8 A(3x−1)=3y\begin{aligned} \dfrac{2}{3}x-\dfrac{4}{3}y&=8\ A\left(3x-1\right)&=3y \end{aligned}

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Q. 23x−43y=8 A(3x−1)=3y\begin{aligned} \dfrac{2}{3}x-\dfrac{4}{3}y&=8\ A\left(3x-1\right)&=3y \end{aligned}
  1. Identify Equations: Identify the given system of equations.\newline23x−43y=8A(3x−1)=3y\begin{aligned} \dfrac{2}{3}x-\dfrac{4}{3}y&=8\\ A\left(3x-1\right)&=3y \end{aligned}
  2. Isolate Variable: Isolate one of the variables in one of the equations. Let's isolate y in the second equation.\newlineA(3x−1)=3yA(3x-1) = 3y\newliney=A(3x−1)3y = \frac{A(3x-1)}{3}
  3. Substitute Expression: Substitute the expression for y into the first equation.\newline23x−43(A(3x−1)3)=8\frac{2}{3}x - \frac{4}{3}\left(\frac{A(3x-1)}{3}\right) = 8
  4. Simplify Equation: Simplify the equation by distributing the −43-\frac{4}{3} and combining like terms.\newline23x−4A(3x−1)9=8\frac{2}{3}x - \frac{4A(3x-1)}{9} = 8\newline23x−4A⋅3x9+4A9=8\frac{2}{3}x - \frac{4A \cdot 3x}{9} + \frac{4A}{9} = 8\newline23x−4A⋅3x9=8−4A9\frac{2}{3}x - \frac{4A \cdot 3x}{9} = 8 - \frac{4A}{9}
  5. Combine X Terms: Combine the x terms by finding a common denominator.\newline2⋅3−4A⋅3x9=8−4A9\frac{2 \cdot 3 - 4A \cdot 3x}{9} = 8 - \frac{4A}{9}\newline6x−12Ax9=8−4A9\frac{6x - 12Ax}{9} = 8 - \frac{4A}{9}
  6. Simplify X Terms: Simplify the x terms.\newline6−12A9x=8−4A9\frac{6 - 12A}{9}x = 8 - \frac{4A}{9}
  7. Solve for X: Solve for x by dividing both sides by 6−12A9\frac{6 - 12A}{9}.\newlinex=8−4A96−12A9x = \frac{8 - \frac{4A}{9}}{\frac{6 - 12A}{9}}\newlinex=8⋅9−4A6−12Ax = \frac{8 \cdot 9 - 4A}{6 - 12A}\newlinex=72−4A6−12Ax = \frac{72 - 4A}{6 - 12A}
  8. Substitute X Value: Now, substitute the value of x back into the expression for y.\newliney=A(3x−1)3y = \frac{A(3x-1)}{3}\newliney=A(3(72−4A6−12A)−1)3y = \frac{A(3\left(\frac{72 - 4A}{6 - 12A}\right)-1)}{3}
  9. Simplify Y Expression: Simplify the expression for y.\newliney=A(3(72−4A6−12A)−1)3y = \frac{A(3\left(\frac{72 - 4A}{6 - 12A}\right)-1)}{3}\newliney=A(216−12A−(6−12A))3(6−12A)y = \frac{A(216 - 12A - (6 - 12A))}{3(6 - 12A)}\newliney=A(216−12A+12A−6)18−36Ay = \frac{A(216 - 12A + 12A - 6)}{18 - 36A}\newliney=A(210)18−36Ay = \frac{A(210)}{18 - 36A}\newliney=210A18−36Ay = \frac{210A}{18 - 36A}

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