Find All Complex Solutions 4a+2b=10

$4 a + 2 b = 10$

Step 1

Subtract $2 b$ from both sides of the equation.

$4 a = 10 - 2 b$

Step 2

Divide each term in $4 a = 10 - 2 b$ by $4$ and simplify.

Divide each term in $4 a = 10 - 2 b$ by $4$ .

$\frac{4 a}{4} = \frac{10}{4} + \frac{- 2 b}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 a}{4} = \frac{10}{4} + \frac{- 2 b}{4}$

Divide $a$ by $1$ .

$a = \frac{10}{4} + \frac{- 2 b}{4}$

Simplify the right side.

Simplify each term.

Cancel the common factor of $10$ and $4$ .

Factor $2$ out of $10$ .

$a = \frac{2 (5)}{4} + \frac{- 2 b}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$a = \frac{2 \cdot 5}{2 \cdot 2} + \frac{- 2 b}{4}$

Cancel the common factor.

$a = \frac{2 \cdot 5}{2 \cdot 2} + \frac{- 2 b}{4}$

Rewrite the expression.

$a = \frac{5}{2} + \frac{- 2 b}{4}$

Cancel the common factor of $- 2$ and $4$ .

Factor $2$ out of $- 2 b$ .

$a = \frac{5}{2} + \frac{2 (- b)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$a = \frac{5}{2} + \frac{2 (- b)}{2 (2)}$

Cancel the common factor.

$a = \frac{5}{2} + \frac{2 (- b)}{2 \cdot 2}$

Rewrite the expression.

$a = \frac{5}{2} + \frac{- b}{2}$

Move the negative in front of the fraction.

$a = \frac{5}{2} - \frac{b}{2}$