begin{array}{l}frac{1}{2} x-frac{2}{3} y=6 frac{1}{4} x+frac{1}{3} y=-1end{array}

Question

begin{array}{l}frac{1}{2} x-frac{2}{3} y=6  frac{1}{4} x+frac{1}{3} y=-1end{array}

Accepted Answer

Step:1 ：(frac{1}{2}x - frac{2}{3}y = 6) and (frac{1}{4}x + frac{1}{3}y = -1)Step:2 ：Multiply the second equation by 2 to make the coefficients of x the same: (frac{1}{2}x + frac{2}{3}y = -2)Step:3 ：Add the two equations: (frac{1}{2}x - frac{2}{3}y + frac{1}{2}x + frac{2}{3}y = 6 - 2)Step:4 ：Simplify: (x = 4)Step:5 ：Substitute x back into the first equation: (frac{1}{2}(4) - frac{2}{3}y = 6)Step:6 ：Simplify: (2 - frac{2}{3}y = 6)Step:7 ：Subtract 2 from both sides: (-frac{2}{3}y = 4)Step:8 ：Multiply both sides by (-frac{3}{2}): (y = -6)Step:9 ：(boxed{x = 4, y = -6})

Answer

Step: 1 ：(frac{1}{2}x - frac{2}{3}y = 6) and (frac{1}{4}x + frac{1}{3}y = -1)Step: 2 ：Multiply the second equation by 2 to make the coefficients of x the same: (frac{1}{2}x + frac{2}{3}y = -2)Step: 3 ：Add the two equations: (frac{1}{2}x - frac{2}{3}y + frac{1}{2}x + frac{2}{3}y = 6 - 2)Step: 4 ：Simplify: (x = 4)Step: 5 ：Substitute x back into the first equation: (frac{1}{2}(4) - frac{2}{3}y = 6)Step: 6 ：Simplify: (2 - frac{2}{3}y = 6)Step: 7 ：Subtract 2 from both sides: (-frac{2}{3}y = 4)Step: 8 ：Multiply both sides by (-frac{3}{2}): (y = -6)Step: 9 ：(boxed{x = 4, y = -6})

$\begin{array}{l} \frac{1}{2} x - \frac{2}{3} y = 6 \\ \frac{1}{4} x + \frac{1}{3} y = - 1 \end{array}$

Answer

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$\begin{array}{l} \frac{1}{2} x - \frac{2}{3} y = 6 \\ \frac{1}{4} x + \frac{1}{3} y = - 1 \end{array}$