Solve by Addition/Elimination 5x-7y=16 and x+7y=8

$5 x - 7 y = 16$ and $x + 7 y = 8$

Step 1

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

$5 x - 7 y = 16$

$(- 5) \cdot (x + 7 y) = (- 5) (8)$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 5) \cdot (x + 7 y)$ .

Apply the distributive property.

$5 x - 7 y = 16$

$- 5 x - 5 (7 y) = (- 5) (8)$

Multiply $7$ by $- 5$ .

$5 x - 7 y = 16$

$- 5 x - 35 y = (- 5) (8)$

$5 x - 7 y = 16$

$- 5 x - 35 y = (- 5) (8)$

$5 x - 7 y = 16$

$- 5 x - 35 y = (- 5) (8)$

Simplify the right side.

Multiply $- 5$ by $8$ .

$5 x - 7 y = 16$

$- 5 x - 35 y = - 40$

$5 x - 7 y = 16$

$- 5 x - 35 y = - 40$

$5 x - 7 y = 16$

$- 5 x - 35 y = - 40$

Step 3

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

		$5$	$x$		$-$	$7$	$y$	$=$		$1$	$6$
$+$	$-$	$5$	$x$	$-$	$3$	$5$	$y$	$=$	$-$	$4$	$0$
				$-$	$4$	$2$	$y$	$=$	$-$	$2$	$4$

Step 4

Divide each term in $- 42 y = - 24$ by $- 42$ and simplify.

Divide each term in $- 42 y = - 24$ by $- 42$ .

$\frac{- 42 y}{- 42} = \frac{- 24}{- 42}$

Simplify the left side.

Cancel the common factor of $- 42$ .

Cancel the common factor.

$\frac{- 42 y}{- 42} = \frac{- 24}{- 42}$

Divide $y$ by $1$ .

$y = \frac{- 24}{- 42}$

Simplify the right side.

Cancel the common factor of $- 24$ and $- 42$ .

Factor $- 6$ out of $- 24$ .

$y = \frac{- 6 (4)}{- 42}$

Cancel the common factors.

Factor $- 6$ out of $- 42$ .

$y = \frac{- 6 \cdot 4}{- 6 \cdot 7}$

Cancel the common factor.

$y = \frac{- 6 \cdot 4}{- 6 \cdot 7}$

Rewrite the expression.

$y = \frac{4}{7}$

Step 5

Substitute the value found for $y$ into one of the original equations, then solve for $x$ .

Substitute the value found for $y$ into one of the original equations to solve for $x$ .

$5 x - 7 (\frac{4}{7}) = 16$

Simplify each term.

Cancel the common factor of $7$ .

Factor $7$ out of $- 7$ .

$5 x + 7 (- 1) \frac{4}{7} = 16$

Cancel the common factor.

$5 x + 7 \cdot - 1 \frac{4}{7} = 16$

Rewrite the expression.

$5 x - 1 \cdot 4 = 16$

Multiply $- 1$ by $4$ .

$5 x - 4 = 16$

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

Add $4$ to both sides of the equation.

$5 x = 16 + 4$

Add $16$ and $4$ .

$5 x = 20$

Divide each term in $5 x = 20$ by $5$ and simplify.

Divide each term in $5 x = 20$ by $5$ .

$\frac{5 x}{5} = \frac{20}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{20}{5}$

Divide $x$ by $1$ .

$x = \frac{20}{5}$

Simplify the right side.

Divide $20$ by $5$ .

$x = 4$

Step 6

The solution to the independent system of equations can be represented as a point.

$(4, \frac{4}{7})$

Step 7

The result can be shown in multiple forms.

Point Form:

$(4, \frac{4}{7})$

Equation Form:

$x = 4, y = \frac{4}{7}$

Step 8

Solve by Addition/Elimination 5x-7y=16 and x+7y=8

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