Solve the System of Equations 1/2a+b=-2 a-2b=8

$\frac{1}{2} a + b = - 2$ $a - 2 b = 8$

Step 1

Add $2 b$ to both sides of the equation.

$a = 8 + 2 b$

$\frac{1}{2} a + b = - 2$

Step 2

Replace all occurrences of $a$ with $8 + 2 b$ in each equation.

Replace all occurrences of $a$ in $\frac{1}{2} a + b = - 2$ with $8 + 2 b$ .

$\frac{1}{2} \cdot (8 + 2 b) + b = - 2$

$a = 8 + 2 b$

Simplify the left side.

Simplify $\frac{1}{2} \cdot (8 + 2 b) + b$ .

Simplify each term.

Apply the distributive property.

$\frac{1}{2} \cdot 8 + \frac{1}{2} \cdot (2 b) + b = - 2$

$a = 8 + 2 b$

Cancel the common factor of $2$ .

Factor $2$ out of $8$ .

$\frac{1}{2} \cdot (2 (4)) + \frac{1}{2} \cdot (2 b) + b = - 2$

$a = 8 + 2 b$

Cancel the common factor.

$\frac{1}{2} \cdot (2 \cdot 4) + \frac{1}{2} \cdot (2 b) + b = - 2$

$a = 8 + 2 b$

Rewrite the expression.

$4 + \frac{1}{2} \cdot (2 b) + b = - 2$

$a = 8 + 2 b$

$4 + \frac{1}{2} \cdot (2 b) + b = - 2$

$a = 8 + 2 b$

Cancel the common factor of $2$ .

Factor $2$ out of $2 b$ .

$4 + \frac{1}{2} \cdot (2 (b)) + b = - 2$

$a = 8 + 2 b$

Cancel the common factor.

$4 + \frac{1}{2} \cdot (2 b) + b = - 2$

$a = 8 + 2 b$

Rewrite the expression.

$4 + b + b = - 2$

$a = 8 + 2 b$

$4 + b + b = - 2$

$a = 8 + 2 b$

$4 + b + b = - 2$

$a = 8 + 2 b$

Add $b$ and $b$ .

$4 + 2 b = - 2$

$a = 8 + 2 b$

$4 + 2 b = - 2$

$a = 8 + 2 b$

$4 + 2 b = - 2$

$a = 8 + 2 b$

$4 + 2 b = - 2$

$a = 8 + 2 b$

Step 3

Solve for $b$ in $4 + 2 b = - 2$ .

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

Subtract $4$ from both sides of the equation.

$2 b = - 2 - 4$

$a = 8 + 2 b$

Subtract $4$ from $- 2$ .

$2 b = - 6$

$a = 8 + 2 b$

$2 b = - 6$

$a = 8 + 2 b$

Divide each term in $2 b = - 6$ by $2$ and simplify.

Divide each term in $2 b = - 6$ by $2$ .

$\frac{2 b}{2} = \frac{- 6}{2}$

$a = 8 + 2 b$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 b}{2} = \frac{- 6}{2}$

$a = 8 + 2 b$

Divide $b$ by $1$ .

$b = \frac{- 6}{2}$

$a = 8 + 2 b$

$b = \frac{- 6}{2}$

$a = 8 + 2 b$

$b = \frac{- 6}{2}$

$a = 8 + 2 b$

Simplify the right side.

Divide $- 6$ by $2$ .

$b = - 3$

$a = 8 + 2 b$

$b = - 3$

$a = 8 + 2 b$

$b = - 3$

$a = 8 + 2 b$

$b = - 3$

$a = 8 + 2 b$

Step 4

Replace all occurrences of $b$ with $- 3$ in each equation.

Replace all occurrences of $b$ in $a = 8 + 2 b$ with $- 3$ .

$a = 8 + 2 (- 3)$

$b = - 3$

Simplify the right side.

Simplify $8 + 2 (- 3)$ .

Multiply $2$ by $- 3$ .

$a = 8 - 6$

$b = - 3$

Subtract $6$ from $8$ .

$a = 2$

$b = - 3$

$a = 2$

$b = - 3$

$a = 2$

$b = - 3$

$a = 2$

$b = - 3$

Step 5

List all of the solutions.

$a = 2, b = - 3$

Solve the System of Equations 1/2a+b=-2 a-2b=8

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