Solve by Graphing (x+3)/4+(y-1)/3=1 , 2x-y=12

$\frac{x + 3}{4} + \frac{y - 1}{3} = 1$ , $2 x - y = 12$

Step 1

Simplify $\frac{x + 3}{4} + \frac{y - 1}{3}$ .

To write $\frac{x + 3}{4}$ as a fraction with a common denominator, multiply by $\frac{3}{3}$ .

$\frac{x + 3}{4} \cdot \frac{3}{3} + \frac{y - 1}{3} = 1$

$2 x - y = 12$

To write $\frac{y - 1}{3}$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$\frac{x + 3}{4} \cdot \frac{3}{3} + \frac{y - 1}{3} \cdot \frac{4}{4} = 1$

$2 x - y = 12$

Write each expression with a common denominator of $12$ , by multiplying each by an appropriate factor of $1$ .

Multiply $\frac{x + 3}{4}$ by $\frac{3}{3}$ .

$\frac{(x + 3) \cdot 3}{4 \cdot 3} + \frac{y - 1}{3} \cdot \frac{4}{4} = 1$

$2 x - y = 12$

Multiply $4$ by $3$ .

$\frac{(x + 3) \cdot 3}{12} + \frac{y - 1}{3} \cdot \frac{4}{4} = 1$

$2 x - y = 12$

Multiply $\frac{y - 1}{3}$ by $\frac{4}{4}$ .

$\frac{(x + 3) \cdot 3}{12} + \frac{(y - 1) \cdot 4}{3 \cdot 4} = 1$

$2 x - y = 12$

Multiply $3$ by $4$ .

$\frac{(x + 3) \cdot 3}{12} + \frac{(y - 1) \cdot 4}{12} = 1$

$2 x - y = 12$

$\frac{(x + 3) \cdot 3}{12} + \frac{(y - 1) \cdot 4}{12} = 1$

$2 x - y = 12$

Combine the numerators over the common denominator.

$\frac{(x + 3) \cdot 3 + (y - 1) \cdot 4}{12} = 1$

$2 x - y = 12$

Simplify the numerator.

Apply the distributive property.

$\frac{x \cdot 3 + 3 \cdot 3 + (y - 1) \cdot 4}{12} = 1$

$2 x - y = 12$

Move $3$ to the left of $x$ .

$\frac{3 \cdot x + 3 \cdot 3 + (y - 1) \cdot 4}{12} = 1$

$2 x - y = 12$

Multiply $3$ by $3$ .

$\frac{3 \cdot x + 9 + (y - 1) \cdot 4}{12} = 1$

$2 x - y = 12$

Apply the distributive property.

$\frac{3 x + 9 + y \cdot 4 - 1 \cdot 4}{12} = 1$

$2 x - y = 12$

Move $4$ to the left of $y$ .

$\frac{3 x + 9 + 4 \cdot y - 1 \cdot 4}{12} = 1$

$2 x - y = 12$

Multiply $- 1$ by $4$ .

$\frac{3 x + 9 + 4 \cdot y - 4}{12} = 1$

$2 x - y = 12$

Subtract $4$ from $9$ .

$\frac{3 x + 4 y + 5}{12} = 1$

$2 x - y = 12$

$\frac{3 x + 4 y + 5}{12} = 1$

$2 x - y = 12$

$\frac{3 x + 4 y + 5}{12} = 1$

$2 x - y = 12$

Step 2

Multiply both sides by $12$ .

$\frac{3 x + 4 y + 5}{12} \cdot 12 = 1 \cdot 12$

$2 x - y = 12$

Step 3

Simplify.

Simplify the left side.

Cancel the common factor of $12$ .

Cancel the common factor.

$\frac{3 x + 4 y + 5}{12} \cdot 12 = 1 \cdot 12$

$2 x - y = 12$

Rewrite the expression.

$3 x + 4 y + 5 = 1 \cdot 12$

$2 x - y = 12$

$3 x + 4 y + 5 = 1 \cdot 12$

$2 x - y = 12$

$3 x + 4 y + 5 = 1 \cdot 12$

$2 x - y = 12$

Simplify the right side.

Multiply $12$ by $1$ .

$3 x + 4 y + 5 = 12$

$2 x - y = 12$

$3 x + 4 y + 5 = 12$

$2 x - y = 12$

$3 x + 4 y + 5 = 12$

$2 x - y = 12$

Step 4

Solve for $y$ .

Move all terms not containing $y$ to the right side of the equation.

Subtract $3 x$ from both sides of the equation.

$4 y + 5 = 12 - 3 x$

$2 x - y = 12$

Subtract $5$ from both sides of the equation.

$4 y = 12 - 3 x - 5$

$2 x - y = 12$

Subtract $5$ from $12$ .

$4 y = - 3 x + 7$

$2 x - y = 12$

$4 y = - 3 x + 7$

$2 x - y = 12$

Divide each term in $4 y = - 3 x + 7$ by $4$ and simplify.

Divide each term in $4 y = - 3 x + 7$ by $4$ .

$\frac{4 y}{4} = \frac{- 3 x}{4} + \frac{7}{4}$

$2 x - y = 12$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{- 3 x}{4} + \frac{7}{4}$

$2 x - y = 12$

Divide $y$ by $1$ .

$y = \frac{- 3 x}{4} + \frac{7}{4}$

$2 x - y = 12$

$y = \frac{- 3 x}{4} + \frac{7}{4}$

$2 x - y = 12$

$y = \frac{- 3 x}{4} + \frac{7}{4}$

$2 x - y = 12$

Simplify the right side.

Move the negative in front of the fraction.