Solve by Graphing 3x+y=16 , 12x+4y=64

$3 x + y = 16$ , $12 x + 4 y = 64$

Step 1

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

$y = 16 - 3 x$

$12 x + 4 y = 64$

Step 2

Subtract $12 x$ from both sides of the equation.

$4 y = 64 - 12 x$

$y = 16 - 3 x$

Step 3

Divide each term in $4 y = 64 - 12 x$ by $4$ and simplify.

Divide each term in $4 y = 64 - 12 x$ by $4$ .

$\frac{4 y}{4} = \frac{64}{4} + \frac{- 12 x}{4}$

$y = 16 - 3 x$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 y}{4} = \frac{64}{4} + \frac{- 12 x}{4}$

$y = 16 - 3 x$

Divide $y$ by $1$ .

$y = \frac{64}{4} + \frac{- 12 x}{4}$

$y = 16 - 3 x$

$y = \frac{64}{4} + \frac{- 12 x}{4}$

$y = 16 - 3 x$

$y = \frac{64}{4} + \frac{- 12 x}{4}$

$y = 16 - 3 x$

Simplify the right side.

Simplify each term.

Divide $64$ by $4$ .

$y = 16 + \frac{- 12 x}{4}$

$y = 16 - 3 x$

Cancel the common factor of $- 12$ and $4$ .

Factor $4$ out of $- 12 x$ .

$y = 16 + \frac{4 (- 3 x)}{4}$

$y = 16 - 3 x$

Cancel the common factors.

Factor $4$ out of $4$ .

$y = 16 + \frac{4 (- 3 x)}{4 (1)}$

$y = 16 - 3 x$

Cancel the common factor.

$y = 16 + \frac{4 (- 3 x)}{4 \cdot 1}$

$y = 16 - 3 x$

Rewrite the expression.

$y = 16 + \frac{- 3 x}{1}$

$y = 16 - 3 x$

Divide $- 3 x$ by $1$ .

$y = 16 - 3 x$

Step 4

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

$y = - 3 x + 16$

Step 5

Solve by Graphing 3x+y=16 , 12x+4y=64

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