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

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

Step 1

Move all terms containing variables to the left.

Subtract $x$ from both sides of the equation.

$y - x = - 2, y = 4 x - 5$

Subtract $4 x$ from both sides of the equation.

$y - x = - 2, y - 4 x = - 5$

Step 2

Reorder the polynomial.

$- x + y = - 2$

$y - 4 x = - 5$

Step 3

Reorder the polynomial.

$- 4 x + y = - 5$

$- x + y = - 2$

Step 4

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

$- x + y = - 2$

$(- 1) \cdot (- 4 x + y) = (- 1) (- 5)$

Step 5

Simplify.

Simplify the left side.

Simplify $(- 1) \cdot (- 4 x + y)$ .

Apply the distributive property.

$- x + y = - 2$

$- 1 (- 4 x) - 1 y = (- 1) (- 5)$

Simplify the expression.

Multiply $- 4$ by $- 1$ .

$- x + y = - 2$

$4 x - 1 y = (- 1) (- 5)$

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

$- x + y = - 2$

$4 x - y = (- 1) (- 5)$

$- x + y = - 2$

$4 x - y = (- 1) (- 5)$

$- x + y = - 2$

$4 x - y = (- 1) (- 5)$

$- x + y = - 2$

$4 x - y = (- 1) (- 5)$

Simplify the right side.

Multiply $- 1$ by $- 5$ .

$- x + y = - 2$

$4 x - y = 5$

$- x + y = - 2$

$4 x - y = 5$

$- x + y = - 2$

$4 x - y = 5$

Step 6

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

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

Step 7

Divide each term in $3 x = 3$ by $3$ and simplify.

Divide each term in $3 x = 3$ by $3$ .

$\frac{3 x}{3} = \frac{3}{3}$

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$\frac{3 x}{3} = \frac{3}{3}$

Divide $x$ by $1$ .

$x = \frac{3}{3}$

Simplify the right side.

Divide $3$ by $3$ .

$x = 1$

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 $y$ .

$- (1) + y = - 2$

Multiply $- 1$ by $1$ .

$- 1 + y = - 2$

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

Add $1$ to both sides of the equation.

$y = - 2 + 1$

Add $- 2$ and $1$ .

$y = - 1$

Step 9

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

$(1, - 1)$

Step 10

The result can be shown in multiple forms.

Point Form:

$(1, - 1)$

Equation Form:

$x = 1, y = - 1$

Step 11

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

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