Solve the System of Equations y=1/2x+3 2x+y=-2

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

Step 1

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

$y = \frac{x}{2} + 3$

$2 x + y = - 2$

Step 2

Replace all occurrences of $y$ with $\frac{x}{2} + 3$ in each equation.

Replace all occurrences of $y$ in $2 x + y = - 2$ with $\frac{x}{2} + 3$ .

$2 x + \frac{x}{2} + 3 = - 2$

$y = \frac{x}{2} + 3$

Simplify the left side.

Simplify $2 x + \frac{x}{2} + 3$ .

Remove parentheses.

$2 x + \frac{x}{2} + 3 = - 2$

$y = \frac{x}{2} + 3$

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

$2 x \cdot \frac{2}{2} + \frac{x}{2} + 3 = - 2$

$y = \frac{x}{2} + 3$

Simplify terms.

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

$\frac{2 x \cdot 2}{2} + \frac{x}{2} + 3 = - 2$

$y = \frac{x}{2} + 3$

Combine the numerators over the common denominator.

$\frac{2 x \cdot 2 + x}{2} + 3 = - 2$

$y = \frac{x}{2} + 3$

$\frac{2 x \cdot 2 + x}{2} + 3 = - 2$

$y = \frac{x}{2} + 3$

Simplify each term.

Simplify the numerator.

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

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

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

$y = \frac{x}{2} + 3$

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

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

$y = \frac{x}{2} + 3$

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

$\frac{x (2 \cdot 2) + x \cdot 1}{2} + 3 = - 2$

$y = \frac{x}{2} + 3$

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

$\frac{x (2 \cdot 2 + 1)}{2} + 3 = - 2$

$y = \frac{x}{2} + 3$

$\frac{x (2 \cdot 2 + 1)}{2} + 3 = - 2$

$y = \frac{x}{2} + 3$

Multiply $2$ by $2$ .

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

$y = \frac{x}{2} + 3$

Add $4$ and $1$ .

$\frac{x \cdot 5}{2} + 3 = - 2$

$y = \frac{x}{2} + 3$

$\frac{x \cdot 5}{2} + 3 = - 2$

$y = \frac{x}{2} + 3$

Move $5$ to the left of $x$ .

$\frac{5 x}{2} + 3 = - 2$

$y = \frac{x}{2} + 3$

$\frac{5 x}{2} + 3 = - 2$

$y = \frac{x}{2} + 3$

$\frac{5 x}{2} + 3 = - 2$

$y = \frac{x}{2} + 3$

$\frac{5 x}{2} + 3 = - 2$

$y = \frac{x}{2} + 3$

$\frac{5 x}{2} + 3 = - 2$

$y = \frac{x}{2} + 3$

Step 3

Solve for $x$ in $\frac{5 x}{2} + 3 = - 2$ .

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

Subtract $3$ from both sides of the equation.

$\frac{5 x}{2} = - 2 - 3$

$y = \frac{x}{2} + 3$

Subtract $3$ from $- 2$ .

$\frac{5 x}{2} = - 5$

$y = \frac{x}{2} + 3$

$\frac{5 x}{2} = - 5$

$y = \frac{x}{2} + 3$

Multiply both sides of the equation by $\frac{2}{5}$ .

$\frac{2}{5} \cdot \frac{5 x}{2} = \frac{2}{5} \cdot - 5$

$y = \frac{x}{2} + 3$

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{2}{5} \cdot \frac{5 x}{2}$ .

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2}{5} \cdot \frac{5 x}{2} = \frac{2}{5} \cdot - 5$

$y = \frac{x}{2} + 3$

Rewrite the expression.

$\frac{1}{5} \cdot (5 x) = \frac{2}{5} \cdot - 5$

$y = \frac{x}{2} + 3$

$\frac{1}{5} \cdot (5 x) = \frac{2}{5} \cdot - 5$

$y = \frac{x}{2} + 3$

Cancel the common factor of $5$ .

Factor $5$ out of $5 x$ .

$\frac{1}{5} \cdot (5 (x)) = \frac{2}{5} \cdot - 5$

$y = \frac{x}{2} + 3$

Cancel the common factor.

$\frac{1}{5} \cdot (5 x) = \frac{2}{5} \cdot - 5$

$y = \frac{x}{2} + 3$

Rewrite the expression.

$x = \frac{2}{5} \cdot - 5$

$y = \frac{x}{2} + 3$

$x = \frac{2}{5} \cdot - 5$

$y = \frac{x}{2} + 3$

$x = \frac{2}{5} \cdot - 5$

$y = \frac{x}{2} + 3$

$x = \frac{2}{5} \cdot - 5$

$y = \frac{x}{2} + 3$

Simplify the right side.

Simplify $\frac{2}{5} \cdot - 5$ .

Cancel the common factor of $5$ .

Factor $5$ out of $- 5$ .

$x = \frac{2}{5} \cdot (5 (- 1))$

$y = \frac{x}{2} + 3$

Cancel the common factor.

$x = \frac{2}{5} \cdot (5 \cdot - 1)$

$y = \frac{x}{2} + 3$

Rewrite the expression.

$x = 2 \cdot - 1$

$y = \frac{x}{2} + 3$

$x = 2 \cdot - 1$

$y = \frac{x}{2} + 3$

Multiply $2$ by $- 1$ .

$x = - 2$

$y = \frac{x}{2} + 3$

$x = - 2$

$y = \frac{x}{2} + 3$

$x = - 2$

$y = \frac{x}{2} + 3$

$x = - 2$

$y = \frac{x}{2} + 3$

$x = - 2$

$y = \frac{x}{2} + 3$

Step 4

Replace all occurrences of $x$ with $- 2$ in each equation.

Replace all occurrences of $x$ in $y = \frac{x}{2} + 3$ with $- 2$ .

$y = \frac{- 2}{2} + 3$

$x = - 2$

Simplify the right side.

Simplify $\frac{- 2}{2} + 3$ .

Divide $- 2$ by $2$ .

$y = - 1 + 3$

$x = - 2$

Add $- 1$ and $3$ .

$y = 2$

$x = - 2$

$y = 2$

$x = - 2$

$y = 2$

$x = - 2$

$y = 2$

$x = - 2$

Step 5

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

$(- 2, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 2, 2)$

Equation Form:

$x = - 2, y = 2$

Step 7

Solve the System of Equations y=1/2x+3 2x+y=-2

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