Solve the System of Equations 3a+b=1 a+b=3

$3 a + b = 1$ $a + b = 3$

Subtract $3 a$ from both sides of the equation.

$b = 1 - 3 a$

$a + b = 3$

Replace all occurrences of $b$ with $1 - 3 a$ in each equation.

Replace all occurrences of $b$ in $a + b = 3$ with $1 - 3 a$ .

$a + 1 - 3 a = 3$

$b = 1 - 3 a$

Simplify the left side.

Simplify $a + 1 - 3 a$ .

Remove parentheses.

$a + 1 - 3 a = 3$

$b = 1 - 3 a$

Subtract $3 a$ from $a$ .

$- 2 a + 1 = 3$

$b = 1 - 3 a$

$- 2 a + 1 = 3$

$b = 1 - 3 a$

$- 2 a + 1 = 3$

$b = 1 - 3 a$

$- 2 a + 1 = 3$

$b = 1 - 3 a$

Solve for $a$ in $- 2 a + 1 = 3$ .

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

Subtract $1$ from both sides of the equation.

$- 2 a = 3 - 1$

$b = 1 - 3 a$

Subtract $1$ from $3$ .

$- 2 a = 2$

$b = 1 - 3 a$

$- 2 a = 2$

$b = 1 - 3 a$

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

Divide each term in $- 2 a = 2$ by $- 2$ .

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

$b = 1 - 3 a$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

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

$b = 1 - 3 a$

Divide $a$ by $1$ .

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

$b = 1 - 3 a$

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

$b = 1 - 3 a$

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

$b = 1 - 3 a$

Simplify the right side.

Divide $2$ by $- 2$ .

$a = - 1$

$b = 1 - 3 a$

$a = - 1$

$b = 1 - 3 a$

$a = - 1$

$b = 1 - 3 a$

$a = - 1$

$b = 1 - 3 a$

Replace all occurrences of $a$ with $- 1$ in each equation.

Replace all occurrences of $a$ in $b = 1 - 3 a$ with $- 1$ .

$b = 1 - 3 \cdot - 1$

$a = - 1$

Simplify the right side.

Simplify $1 - 3 \cdot - 1$ .

Multiply $- 3$ by $- 1$ .

$b = 1 + 3$

$a = - 1$

Add $1$ and $3$ .

$b = 4$

$a = - 1$

$b = 4$

$a = - 1$

$b = 4$

$a = - 1$

$b = 4$

$a = - 1$

List all of the solutions.

$b = 4, a = - 1$

Solve the System of Equations 3a+b=1 a+b=3

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