Solve for x
x=\frac{4\left(y-3\right)}{5}
y\neq 3
Solve for y
y=\frac{5x}{4}+3
x\neq 0
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5\times 2x=8\left(y-3\right)
Multiply both sides of the equation by 5\left(y-3\right), the least common multiple of y-3,5.
10x=8\left(y-3\right)
Multiply 5 and 2 to get 10.
10x=8y-24
Use the distributive property to multiply 8 by y-3.
\frac{10x}{10}=\frac{8y-24}{10}
Divide both sides by 10.
x=\frac{8y-24}{10}
Dividing by 10 undoes the multiplication by 10.
x=\frac{4y-12}{5}
Divide -24+8y by 10.
5\times 2x=8\left(y-3\right)
Variable y cannot be equal to 3 since division by zero is not defined. Multiply both sides of the equation by 5\left(y-3\right), the least common multiple of y-3,5.
10x=8\left(y-3\right)
Multiply 5 and 2 to get 10.
10x=8y-24
Use the distributive property to multiply 8 by y-3.
8y-24=10x
Swap sides so that all variable terms are on the left hand side.
8y=10x+24
Add 24 to both sides.
\frac{8y}{8}=\frac{10x+24}{8}
Divide both sides by 8.
y=\frac{10x+24}{8}
Dividing by 8 undoes the multiplication by 8.
y=\frac{5x}{4}+3
Divide 10x+24 by 8.
y=\frac{5x}{4}+3\text{, }y\neq 3
Variable y cannot be equal to 3.
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