Solve the System of Equations y=1/2x+6 x+6y=12

$y = \frac{1}{2} x + 6$ $x + 6 y = 12$

Step 1

Combine $\frac{1}{2}$ and $x$ .

$y = \frac{x}{2} + 6$

$x + 6 y = 12$

Step 2

Replace all occurrences of $y$ with $\frac{x}{2} + 6$ in each equation.

Replace all occurrences of $y$ in $x + 6 y = 12$ with $\frac{x}{2} + 6$ .

$x + 6 (\frac{x}{2} + 6) = 12$

$y = \frac{x}{2} + 6$

Simplify the left side.

Simplify $x + 6 (\frac{x}{2} + 6)$ .

Simplify each term.

Apply the distributive property.

$x + 6 (\frac{x}{2}) + 6 \cdot 6 = 12$

$y = \frac{x}{2} + 6$

Cancel the common factor of $2$ .

Factor $2$ out of $6$ .

$x + 2 (3) (\frac{x}{2}) + 6 \cdot 6 = 12$

$y = \frac{x}{2} + 6$

Cancel the common factor.

$x + 2 \cdot (3 (\frac{x}{2})) + 6 \cdot 6 = 12$

$y = \frac{x}{2} + 6$

Rewrite the expression.

$x + 3 x + 6 \cdot 6 = 12$

$y = \frac{x}{2} + 6$

$x + 3 x + 6 \cdot 6 = 12$

$y = \frac{x}{2} + 6$

Multiply $6$ by $6$ .

$x + 3 x + 36 = 12$

$y = \frac{x}{2} + 6$

$x + 3 x + 36 = 12$

$y = \frac{x}{2} + 6$

Add $x$ and $3 x$ .

$4 x + 36 = 12$

$y = \frac{x}{2} + 6$

$4 x + 36 = 12$

$y = \frac{x}{2} + 6$

$4 x + 36 = 12$

$y = \frac{x}{2} + 6$

$4 x + 36 = 12$

$y = \frac{x}{2} + 6$

Step 3

Solve for $x$ in $4 x + 36 = 12$ .

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

Subtract $36$ from both sides of the equation.

$4 x = 12 - 36$

$y = \frac{x}{2} + 6$

Subtract $36$ from $12$ .

$4 x = - 24$

$y = \frac{x}{2} + 6$

$4 x = - 24$

$y = \frac{x}{2} + 6$

Divide each term in $4 x = - 24$ by $4$ and simplify.

Divide each term in $4 x = - 24$ by $4$ .

$\frac{4 x}{4} = \frac{- 24}{4}$

$y = \frac{x}{2} + 6$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{- 24}{4}$

$y = \frac{x}{2} + 6$

Divide $x$ by $1$ .

$x = \frac{- 24}{4}$

$y = \frac{x}{2} + 6$

$x = \frac{- 24}{4}$

$y = \frac{x}{2} + 6$

$x = \frac{- 24}{4}$

$y = \frac{x}{2} + 6$

Simplify the right side.

Divide $- 24$ by $4$ .

$x = - 6$

$y = \frac{x}{2} + 6$

$x = - 6$

$y = \frac{x}{2} + 6$

$x = - 6$

$y = \frac{x}{2} + 6$

$x = - 6$

$y = \frac{x}{2} + 6$

Step 4

Replace all occurrences of $x$ with $- 6$ in each equation.

Replace all occurrences of $x$ in $y = \frac{x}{2} + 6$ with $- 6$ .

$y = \frac{- 6}{2} + 6$

$x = - 6$

Simplify the right side.

Simplify $\frac{- 6}{2} + 6$ .

Divide $- 6$ by $2$ .

$y = - 3 + 6$

$x = - 6$

Add $- 3$ and $6$ .

$y = 3$

$x = - 6$

$y = 3$

$x = - 6$

$y = 3$

$x = - 6$

$y = 3$

$x = - 6$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(- 6, 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 6, 3)$

Equation Form:

$x = - 6, y = 3$

Step 7

Solve the System of Equations y=1/2x+6 x+6y=12

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