Solve by Addition/Elimination a+4b=-4 a+10b=-16

$a + 4 b = - 4$ $a + 10 b = - 16$

Step 1

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

$a + 4 b = - 4$

$(- 1) \cdot (a + 10 b) = (- 1) (- 16)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (a + 10 b)$ .

Apply the distributive property.

$a + 4 b = - 4$

$- 1 a - 1 (10 b) = (- 1) (- 16)$

Simplify the expression.

Rewrite $- 1 a$ as $- a$ .

$a + 4 b = - 4$

$- a - 1 (10 b) = (- 1) (- 16)$

Multiply $10$ by $- 1$ .

$a + 4 b = - 4$

$- a - 10 b = (- 1) (- 16)$

$a + 4 b = - 4$

$- a - 10 b = (- 1) (- 16)$

$a + 4 b = - 4$

$- a - 10 b = (- 1) (- 16)$

$a + 4 b = - 4$

$- a - 10 b = (- 1) (- 16)$

Simplify the right side.

Multiply $- 1$ by $- 16$ .

$a + 4 b = - 4$

$- a - 10 b = 16$

$a + 4 b = - 4$

$- a - 10 b = 16$

$a + 4 b = - 4$

$- a - 10 b = 16$

Step 3

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

		$a$	$+$		$4$	$b$	$=$	$-$	$4$
$+$	$-$	$a$	$-$	$1$	$0$	$b$	$=$	$1$	$6$
				$-$	$6$	$b$	$=$	$1$	$2$

Step 4

Divide each term in $- 6 b = 12$ by $- 6$ and simplify.

Divide each term in $- 6 b = 12$ by $- 6$ .

$\frac{- 6 b}{- 6} = \frac{12}{- 6}$

Simplify the left side.

Cancel the common factor of $- 6$ .

Cancel the common factor.

$\frac{- 6 b}{- 6} = \frac{12}{- 6}$

Divide $b$ by $1$ .

$b = \frac{12}{- 6}$

Simplify the right side.

Divide $12$ by $- 6$ .

$b = - 2$

Step 5

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 $a$ .

$a + 4 (- 2) = - 4$

Multiply $4$ by $- 2$ .

$a - 8 = - 4$

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

Add $8$ to both sides of the equation.

$a = - 4 + 8$

Add $- 4$ and $8$ .

$a = 4$

Step 6

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

$b = - 2$

$a = 4$

Solve by Addition/Elimination a+4b=-4 a+10b=-16

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