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

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

Eliminate the equal sides of each equation and combine.

$\frac{1}{2} x = x + 2$

Solve $\frac{1}{2} x = x + 2$ for $x$ .

Simplify $\frac{1}{2} x$ .

Rewrite.

$0 + 0 + \frac{1}{2} x = x + 2$

Simplify by adding zeros.

$\frac{1}{2} x = x + 2$

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

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

Move all terms containing $x$ to the left side of the equation.

Subtract $x$ from both sides of the equation.

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

To write $- x$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{2} - x \cdot \frac{2}{2} = 2$

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

$\frac{x}{2} + \frac{- x \cdot 2}{2} = 2$

Combine the numerators over the common denominator.

$\frac{x - x \cdot 2}{2} = 2$

Simplify the numerator.

Factor $x$ out of $x - x \cdot 2$ .

Raise $x$ to the power of $1$ .

$\frac{x^{1} - x \cdot 2}{2} = 2$

Factor $x$ out of $x^{1}$ .

$\frac{x \cdot 1 - x \cdot 2}{2} = 2$

Factor $x$ out of $- x \cdot 2$ .

$\frac{x \cdot 1 + x (- 1 \cdot 2)}{2} = 2$

Factor $x$ out of $x \cdot 1 + x (- 1 \cdot 2)$ .

$\frac{x (1 - 1 \cdot 2)}{2} = 2$

Multiply $- 1$ by $2$ .

$\frac{x (1 - 2)}{2} = 2$

Subtract $2$ from $1$ .

$\frac{x \cdot - 1}{2} = 2$

Move $- 1$ to the left of $x$ .

$\frac{- 1 \cdot x}{2} = 2$

Move the negative in front of the fraction.

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

Multiply both sides of the equation by $- 2$ .

$- 2 (- \frac{x}{2}) = - 2 \cdot 2$

Simplify both sides of the equation.

Simplify the left side.

Simplify $- 2 (- \frac{x}{2})$ .

Cancel the common factor of $2$ .

Move the leading negative in $- \frac{x}{2}$ into the numerator.

$- 2 \frac{- x}{2} = - 2 \cdot 2$

Factor $2$ out of $- 2$ .

$2 (- 1) \frac{- x}{2} = - 2 \cdot 2$

Cancel the common factor.

$2 \cdot - 1 \frac{- x}{2} = - 2 \cdot 2$

Rewrite the expression.

$- - x = - 2 \cdot 2$

Multiply.

Multiply $- 1$ by $- 1$ .

$1 x = - 2 \cdot 2$

Multiply $x$ by $1$ .

$x = - 2 \cdot 2$

Simplify the right side.

Multiply $- 2$ by $2$ .

$x = - 4$

Evaluate $y$ when $x = - 4$ .

Substitute $- 4$ for $x$ .

$y = (- 4) + 2$

Substitute $- 4$ for $x$ in $y = (- 4) + 2$ and solve for $y$ .

Remove parentheses.

$y = - 4 + 2$

Remove parentheses.

$y = (- 4) + 2$

Add $- 4$ and $2$ .

$y = - 2$

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

$(- 4, - 2)$

The result can be shown in multiple forms.

Point Form:

$(- 4, - 2)$

Equation Form:

$x = - 4, y = - 2$

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

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