\frac{x-y}{2}+\frac{x+y}{3} =4 |6
2x+3y=5(x-3)
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3(x-y)+2(x+y)=24
2x-3y=5x-15
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3x-3y+2x+2y=24
2x-3y-5x=-15
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5x-y=24
-3x-3y=-15 |(-1)
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-y=24-5x |*(-1)
3x-3y=15 |:3
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y=5x-24
x-y=5
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y=5x-24
x-(5x-24)=5
x-5x+24=5 |-24
-4x=-19 |:(-4)
x=\frac{19}{4}
x=4\frac{3}{4}
y=5x-24
y=5*\frac{19}{4}-24
y=\frac{95}{4}-\frac{96}{4}
y=-\frac{1}{4}