Solve by Addition/Elimination x-4y=14 5x-3y=2

$x - 4 y = 14$ $5 x - 3 y = 2$

Step 1

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

$(- 5) \cdot (x - 4 y) = (- 5) (14)$

$5 x - 3 y = 2$

Step 2

Simplify.

Simplify the left side.

Simplify $(- 5) \cdot (x - 4 y)$ .

Apply the distributive property.

$- 5 x - 5 (- 4 y) = (- 5) (14)$

$5 x - 3 y = 2$

Multiply $- 4$ by $- 5$ .

$- 5 x + 20 y = (- 5) (14)$

$5 x - 3 y = 2$

$- 5 x + 20 y = (- 5) (14)$

$5 x - 3 y = 2$

$- 5 x + 20 y = (- 5) (14)$

$5 x - 3 y = 2$

Simplify the right side.

Multiply $- 5$ by $14$ .

$- 5 x + 20 y = - 70$

$5 x - 3 y = 2$

$- 5 x + 20 y = - 70$

$5 x - 3 y = 2$

$- 5 x + 20 y = - 70$

$5 x - 3 y = 2$

Step 3

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

	$-$	$5$	$x$	$+$	$2$	$0$	$y$	$=$	$-$	$7$	$0$
$+$		$5$	$x$		$-$	$3$	$y$	$=$			$2$
					$1$	$7$	$y$	$=$	$-$	$6$	$8$

Step 4

Divide each term in $17 y = - 68$ by $17$ and simplify.

Divide each term in $17 y = - 68$ by $17$ .

$\frac{17 y}{17} = \frac{- 68}{17}$

Simplify the left side.

Cancel the common factor of $17$ .

Cancel the common factor.

$\frac{17 y}{17} = \frac{- 68}{17}$

Divide $y$ by $1$ .

$y = \frac{- 68}{17}$

Simplify the right side.

Divide $- 68$ by $17$ .

$y = - 4$

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 $x$ .

$- 5 x + 20 (- 4) = - 70$

Multiply $20$ by $- 4$ .

$- 5 x - 80 = - 70$

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

Add $80$ to both sides of the equation.

$- 5 x = - 70 + 80$

Add $- 70$ and $80$ .

$- 5 x = 10$

Divide each term in $- 5 x = 10$ by $- 5$ and simplify.

Divide each term in $- 5 x = 10$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{10}{- 5}$

Simplify the left side.

Cancel the common factor of $- 5$ .

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{10}{- 5}$

Divide $x$ by $1$ .

$x = \frac{10}{- 5}$

Simplify the right side.

Divide $10$ by $- 5$ .

$x = - 2$

Step 6

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

$(- 2, - 4)$

Step 7

The result can be shown in multiple forms.

Point Form:

$(- 2, - 4)$

Equation Form:

$x = - 2, y = - 4$

Step 8

Solve by Addition/Elimination x-4y=14 5x-3y=2

Related Questions

Support LCMGCF.com by disabling your adblocker.