Solve -2(x-5)+1(y-3)=0

$$- 2 ( x - 5 ) + 1 ( y - 3 ) = 0$$

Solve for x

$$x=\frac{y+7}{2}$$

Steps for Solving Linear Equation

Use the distributive property to multiply -2 by x-5.

$$-2x+10+1\left(y-3\right)=0$$

Use the distributive property to multiply 1 by y-3.

$$-2x+10+y-3=0$$

Subtract 3 from 10 to get 7.

$$-2x+7+y=0$$

Subtract 7 from both sides. Anything subtracted from zero gives its negation.

$$-2x+y=-7$$

Subtract y from both sides.

$$-2x=-7-y$$

The equation is in standard form.

$$-2x=-y-7$$

Divide both sides by -2.

$$\frac{-2x}{-2}=\frac{-y-7}{-2}$$

Dividing by -2 undoes the multiplication by -2.

$$x=\frac{-y-7}{-2}$$

Divide -7-y by -2.

$$x=\frac{y+7}{2}$$

Solve for y

$$y=2x-7$$

Solution Steps

Use the distributive property to multiply -2 by x-5.

$$-2x+10+1\left(y-3\right)=0$$

Use the distributive property to multiply 1 by y-3.

$$-2x+10+y-3=0$$

Subtract 3 from 10 to get 7.

$$-2x+7+y=0$$

Add 2x to both sides. Anything plus zero gives itself.

$$7+y=2x$$

Subtract 7 from both sides.

$$y=2x-7$$