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

$y = 3 x + 4$ $y = x - 2$

Step 1

Move all terms containing variables to the left side of the equation.

Subtract $3 x$ from both sides of the equation.

$y - 3 x = 4$

$y = x - 2$

Reorder $y$ and $- 3 x$ .

$- 3 x + y = 4$

$y = x - 2$

$- 3 x + y = 4$

$y = x - 2$

Step 2

Move all terms containing variables to the left side of the equation.

Subtract $x$ from both sides of the equation.

$y - x = - 2$

$- 3 x + y = 4$

Reorder $y$ and $- x$ .

$- x + y = - 2$

$- 3 x + y = 4$

$- x + y = - 2$

$- 3 x + y = 4$

Step 3

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

$- 3 x + y = 4$

$(- 1) \cdot (- x + y) = (- 1) (- 2)$

Step 4

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (- x + y)$ .

Apply the distributive property.

$- 3 x + y = 4$

$- 1 (- x) - 1 y = (- 1) (- 2)$

Multiply $- 1 (- x)$ .

Multiply $- 1$ by $- 1$ .

$- 3 x + y = 4$

$1 x - 1 y = (- 1) (- 2)$

Multiply $x$ by $1$ .

$- 3 x + y = 4$

$x - 1 y = (- 1) (- 2)$

$- 3 x + y = 4$

$x - 1 y = (- 1) (- 2)$

Rewrite $- 1 y$ as $- y$ .

$- 3 x + y = 4$

$x - y = (- 1) (- 2)$

$- 3 x + y = 4$

$x - y = (- 1) (- 2)$

$- 3 x + y = 4$

$x - y = (- 1) (- 2)$

Simplify the right side.

Multiply $- 1$ by $- 2$ .

$- 3 x + y = 4$

$x - y = 2$

$- 3 x + y = 4$

$x - y = 2$

$- 3 x + y = 4$

$x - y = 2$

Step 5

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

	$-$	$3$	$x$	$+$	$y$	$=$	$4$
$+$			$x$	$-$	$y$	$=$	$2$
	$-$	$2$	$x$			$=$	$6$

Step 6

Divide each term in $- 2 x = 6$ by $- 2$ and simplify.

Divide each term in $- 2 x = 6$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{6}{- 2}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{6}{- 2}$

Divide $x$ by $1$ .

$x = \frac{6}{- 2}$

Simplify the right side.

Divide $6$ by $- 2$ .

$x = - 3$

Step 7

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 $y$ .

$- 3 \cdot - 3 + y = 4$

Multiply $- 3$ by $- 3$ .

$9 + y = 4$

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

Subtract $9$ from both sides of the equation.

$y = 4 - 9$

Subtract $9$ from $4$ .

$y = - 5$

Step 8

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

$(- 3, - 5)$

Step 9

The result can be shown in multiple forms.

Point Form:

$(- 3, - 5)$

Equation Form:

$x = - 3, y = - 5$

Step 10

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

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