Solve y-3/x-5=-2-(-1)/-3-4

$$\frac { y - 3 } { x - 5 } = \frac { - 2 - ( - 1 ) } { - 3 - 4 }$$

Solve for x

$$x=7y-16$$

$$y\neq 3$$

Steps for Solving Linear Equation

Variable x cannot be equal to 5 since division by zero is not defined. Multiply both sides of the equation by x-5.

$$y-3=\left(-\frac{1}{7}x+\frac{5}{7}\right)\left(-2-\left(-1\right)\right)$$

The opposite of -1 is 1.

$$y-3=\left(-\frac{1}{7}x+\frac{5}{7}\right)\left(-2+1\right)$$

Add -2 and 1 to get -1.

$$y-3=\left(-\frac{1}{7}x+\frac{5}{7}\right)\left(-1\right)$$

Use the distributive property to multiply -\frac{1}{7}x+\frac{5}{7} by -1.

$$y-3=\frac{1}{7}x-\frac{5}{7}$$

Swap sides so that all variable terms are on the left hand side.

$$\frac{1}{7}x-\frac{5}{7}=y-3$$

Add \frac{5}{7} to both sides.

$$\frac{1}{7}x=y-3+\frac{5}{7}$$

Add -3 and \frac{5}{7} to get -\frac{16}{7}.

$$\frac{1}{7}x=y-\frac{16}{7}$$

Multiply both sides by 7.

$$\frac{\frac{1}{7}x}{\frac{1}{7}}=\frac{y-\frac{16}{7}}{\frac{1}{7}}$$

Dividing by \frac{1}{7} undoes the multiplication by \frac{1}{7}.

$$x=\frac{y-\frac{16}{7}}{\frac{1}{7}}$$

Divide y-\frac{16}{7} by \frac{1}{7} by multiplying y-\frac{16}{7} by the reciprocal of \frac{1}{7}.

$$x=7y-16$$

Variable x cannot be equal to 5.

$$x=7y-16\text{, }x\neq 5$$

Solve for y

$$y=\frac{x+16}{7}$$

$$x\neq 5$$

Solution Steps

Multiply both sides of the equation by x-5.

$$y-3=\left(-\frac{1}{7}x+\frac{5}{7}\right)\left(-2-\left(-1\right)\right)$$

The opposite of -1 is 1.

$$y-3=\left(-\frac{1}{7}x+\frac{5}{7}\right)\left(-2+1\right)$$

Add -2 and 1 to get -1.

$$y-3=\left(-\frac{1}{7}x+\frac{5}{7}\right)\left(-1\right)$$

Use the distributive property to multiply -\frac{1}{7}x+\frac{5}{7} by -1.

$$y-3=\frac{1}{7}x-\frac{5}{7}$$

Add 3 to both sides.

$$y=\frac{1}{7}x-\frac{5}{7}+3$$

Add -\frac{5}{7} and 3 to get \frac{16}{7}.

$$y=\frac{1}{7}x+\frac{16}{7}$$