Solve by Addition/Elimination -4y+11x-67=0 2y+5x-19=0

$- 4 y + 11 x - 67 = 0$ $2 y + 5 x - 19 = 0$

Step 1

Simplify the left side.

Reorder $- 4 y$ and $11 x$ .

$11 x - 4 y - 67 = 0$

$2 y + 5 x - 19 = 0$

$11 x - 4 y - 67 = 0$

$2 y + 5 x - 19 = 0$

Step 2

Simplify the left side.

Reorder $2 y$ and $5 x$ .

$5 x + 2 y - 19 = 0$

$11 x - 4 y - 67 = 0$

$5 x + 2 y - 19 = 0$

$11 x - 4 y - 67 = 0$

Step 3

Move all terms containing variables to the left.

Add $67$ to both sides of the equation.

$11 x - 4 y = 67, 5 x + 2 y - 19 = 0$

Add $19$ to both sides of the equation.

$11 x - 4 y = 67, 5 x + 2 y = 19$

Step 4

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

$11 x - 4 y = 67$

$(2) \cdot (5 x + 2 y) = (2) (19)$

Step 5

Simplify.

Simplify the left side.

Simplify $(2) \cdot (5 x + 2 y)$ .

Apply the distributive property.

$11 x - 4 y = 67$

$2 (5 x) + 2 (2 y) = (2) (19)$

Multiply.

Multiply $5$ by $2$ .

$11 x - 4 y = 67$

$10 x + 2 (2 y) = (2) (19)$

Multiply $2$ by $2$ .

$11 x - 4 y = 67$

$10 x + 4 y = (2) (19)$

$11 x - 4 y = 67$

$10 x + 4 y = (2) (19)$

$11 x - 4 y = 67$

$10 x + 4 y = (2) (19)$

$11 x - 4 y = 67$

$10 x + 4 y = (2) (19)$

Simplify the right side.

Multiply $2$ by $19$ .

$11 x - 4 y = 67$

$10 x + 4 y = 38$

$11 x - 4 y = 67$

$10 x + 4 y = 38$

$11 x - 4 y = 67$

$10 x + 4 y = 38$

Step 6

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

	$1$	$1$	$x$	$-$	$4$	$y$	$=$	$6$	$7$
$+$	$1$	$0$	$x$	$+$	$4$	$y$	$=$	$3$	$8$
	$2$	$1$	$x$				$=$	$1$	$0$	$5$

Step 7

Divide each term in $21 x = 105$ by $21$ and simplify.

Divide each term in $21 x = 105$ by $21$ .

$\frac{21 x}{21} = \frac{105}{21}$

Simplify the left side.

Cancel the common factor of $21$ .

Cancel the common factor.

$\frac{21 x}{21} = \frac{105}{21}$

Divide $x$ by $1$ .

$x = \frac{105}{21}$

Simplify the right side.

Divide $105$ by $21$ .

$x = 5$

Step 8

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

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

$11 (5) - 4 y = 67$

Multiply $11$ by $5$ .

$55 - 4 y = 67$

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

Subtract $55$ from both sides of the equation.

$- 4 y = 67 - 55$

Subtract $55$ from $67$ .

$- 4 y = 12$

Divide each term in $- 4 y = 12$ by $- 4$ and simplify.

Divide each term in $- 4 y = 12$ by $- 4$ .

$\frac{- 4 y}{- 4} = \frac{12}{- 4}$

Simplify the left side.

Cancel the common factor of $- 4$ .

Cancel the common factor.

$\frac{- 4 y}{- 4} = \frac{12}{- 4}$

Divide $y$ by $1$ .

$y = \frac{12}{- 4}$

Simplify the right side.

Divide $12$ by $- 4$ .

$y = - 3$

Step 9

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

$(5, - 3)$

Step 10

The result can be shown in multiple forms.

Point Form:

$(5, - 3)$

Equation Form:

$x = 5, y = - 3$

Step 11

Solve by Addition/Elimination -4y+11x-67=0 2y+5x-19=0

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