Solve by Linear Combination a-3b=-1 2a+3b=16

$a - 3 b = - 1$ $2 a + 3 b = 16$

Multiply each equation by the value that makes the coefficients of $a$ opposite.

$(- 2) \cdot (a - 3 b) = (- 2) (- 1)$

$2 a + 3 b = 16$

Simplify.

Simplify the left side.

Simplify $(- 2) \cdot (a - 3 b)$ .

Apply the distributive property.

$- 2 a - 2 (- 3 b) = (- 2) (- 1)$

$2 a + 3 b = 16$

Multiply $- 3$ by $- 2$ .

$- 2 a + 6 b = (- 2) (- 1)$

$2 a + 3 b = 16$

$- 2 a + 6 b = (- 2) (- 1)$

$2 a + 3 b = 16$

$- 2 a + 6 b = (- 2) (- 1)$

$2 a + 3 b = 16$

Simplify the right side.

Multiply $- 2$ by $- 1$ .

$- 2 a + 6 b = 2$

$2 a + 3 b = 16$

$- 2 a + 6 b = 2$

$2 a + 3 b = 16$

$- 2 a + 6 b = 2$

$2 a + 3 b = 16$

Add the two equations together to eliminate $a$ from the system.

	$-$	$2$	$a$	$+$	$6$	$b$	$=$		$2$
$+$		$2$	$a$	$+$	$3$	$b$	$=$	$1$	$6$
					$9$	$b$	$=$	$1$	$8$

Divide each term in $9 b = 18$ by $9$ and simplify.

Divide each term in $9 b = 18$ by $9$ .

$\frac{9 b}{9} = \frac{18}{9}$

Simplify the left side.

Cancel the common factor of $9$ .

Cancel the common factor.

$\frac{9 b}{9} = \frac{18}{9}$

Divide $b$ by $1$ .

$b = \frac{18}{9}$

Simplify the right side.

Divide $18$ by $9$ .

$b = 2$

Substitute the value found for $b$ into one of the original equations, then solve for $a$ .

Substitute the value found for $b$ into one of the original equations to solve for $a$ .

$- 2 a + 6 (2) = 2$

Multiply $6$ by $2$ .

$- 2 a + 12 = 2$

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

Subtract $12$ from both sides of the equation.

$- 2 a = 2 - 12$

Subtract $12$ from $2$ .

$- 2 a = - 10$

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

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

$\frac{- 2 a}{- 2} = \frac{- 10}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 a}{- 2} = \frac{- 10}{- 2}$

Divide $a$ by $1$ .

$a = \frac{- 10}{- 2}$

Simplify the right side.

Divide $- 10$ by $- 2$ .

$a = 5$

This is the final solution to the independent system of equations.

$b = 2$

$a = 5$

Solve by Linear Combination a-3b=-1 2a+3b=16

Related Questions

Support LCMGCF.com by disabling your adblocker.