Solve 3-y/2x=6y-7/4x-5

$$\frac { 3 - y } { 2 x } = \frac { 6 y - 7 } { 4 x - 5 }$$

Solve for x

$$x=-\frac{5\left(y-3\right)}{2\left(13-8y\right)}$$

$$y\neq 3\text{ and }y\neq \frac{13}{8}\text{ and }y\neq \frac{7}{6}$$

Steps for Solving Linear Equation

Variable x cannot be equal to any of the values 0,\frac{5}{4} since division by zero is not defined. Multiply both sides of the equation by 2x\left(4x-5\right), the least common multiple of 2x,4x-5.

$$\left(4x-5\right)\left(3-y\right)=2x\left(6y-7\right)$$

Use the distributive property to multiply 4x-5 by 3-y.

$$12x-4yx-15+5y=2x\left(6y-7\right)$$

Use the distributive property to multiply 2x by 6y-7.

$$12x-4yx-15+5y=12yx-14x$$

Subtract 12yx from both sides.

$$12x-4yx-15+5y-12yx=-14x$$

Combine -4yx and -12yx to get -16yx.

$$12x-16yx-15+5y=-14x$$

Add 14x to both sides.

$$12x-16yx-15+5y+14x=0$$

Combine 12x and 14x to get 26x.

$$26x-16yx-15+5y=0$$

Add 15 to both sides. Anything plus zero gives itself.

$$26x-16yx+5y=15$$

Subtract 5y from both sides.

$$26x-16yx=15-5y$$

Combine all terms containing x.

$$\left(26-16y\right)x=15-5y$$

Divide both sides by -16y+26.

$$\frac{\left(26-16y\right)x}{26-16y}=\frac{15-5y}{26-16y}$$

Dividing by -16y+26 undoes the multiplication by -16y+26.

$$x=\frac{15-5y}{26-16y}$$

Divide 15-5y by -16y+26.

$$x=\frac{5\left(3-y\right)}{2\left(13-8y\right)}$$

Variable x cannot be equal to any of the values \frac{5}{4},0.

$$x=\frac{5\left(3-y\right)}{2\left(13-8y\right)}\text{, }x\neq \frac{5}{4}\text{ and }x\neq 0$$

Solve for y

$$y=-\frac{26x-15}{5-16x}$$

$$x\neq \frac{5}{16}\text{ and }x\neq 0\text{ and }x\neq \frac{5}{4}$$

Steps for Solving Linear Equation

Multiply both sides of the equation by 2x\left(4x-5\right), the least common multiple of 2x,4x-5.

$$\left(4x-5\right)\left(3-y\right)=2x\left(6y-7\right)$$

Use the distributive property to multiply 4x-5 by 3-y.

$$12x-4yx-15+5y=2x\left(6y-7\right)$$

Use the distributive property to multiply 2x by 6y-7.

$$12x-4yx-15+5y=12yx-14x$$

Subtract 12yx from both sides.

$$12x-4yx-15+5y-12yx=-14x$$

Combine -4yx and -12yx to get -16yx.

$$12x-16yx-15+5y=-14x$$

Subtract 12x from both sides.

$$-16yx-15+5y=-14x-12x$$

Combine -14x and -12x to get -26x.

$$-16yx-15+5y=-26x$$

Add 15 to both sides.

$$-16yx+5y=-26x+15$$

Combine all terms containing y.

$$\left(-16x+5\right)y=-26x+15$$

The equation is in standard form.

$$\left(5-16x\right)y=15-26x$$

Divide both sides by 5-16x.

$$\frac{\left(5-16x\right)y}{5-16x}=\frac{15-26x}{5-16x}$$

Dividing by 5-16x undoes the multiplication by 5-16x.

$$y=\frac{15-26x}{5-16x}$$