Solve by Addition/Elimination 2x-3y=-1 y=x-1

$2 x - 3 y = - 1$ $y = x - 1$

Step 1

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

Subtract $x$ from both sides of the equation.

$y - x = - 1$

$2 x - 3 y = - 1$

Reorder $y$ and $- x$ .

$- x + y = - 1$

$2 x - 3 y = - 1$

$- x + y = - 1$

$2 x - 3 y = - 1$

Step 2

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

$2 x - 3 y = - 1$

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

Step 3

Simplify.

Simplify the left side.

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

Apply the distributive property.

$2 x - 3 y = - 1$

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

Multiply $- 1$ by $2$ .

$2 x - 3 y = - 1$

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

$2 x - 3 y = - 1$

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

$2 x - 3 y = - 1$

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

Simplify the right side.

Multiply $2$ by $- 1$ .

$2 x - 3 y = - 1$

$- 2 x + 2 y = - 2$

$2 x - 3 y = - 1$

$- 2 x + 2 y = - 2$

$2 x - 3 y = - 1$

$- 2 x + 2 y = - 2$

Step 4

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

		$2$	$x$	$-$	$3$	$y$	$=$	$-$	$1$
$+$	$-$	$2$	$x$	$+$	$2$	$y$	$=$	$-$	$2$
					$-$	$y$	$=$	$-$	$3$

Step 5

Divide each term in $- y = - 3$ by $- 1$ and simplify.

Divide each term in $- y = - 3$ by $- 1$ .

$\frac{- y}{- 1} = \frac{- 3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{- 3}{- 1}$

Divide $y$ by $1$ .

$y = \frac{- 3}{- 1}$

Simplify the right side.

Divide $- 3$ by $- 1$ .

$y = 3$

Step 6

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 $x$ .

$2 x - 3 \cdot 3 = - 1$

Multiply $- 3$ by $3$ .

$2 x - 9 = - 1$

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

Add $9$ to both sides of the equation.

$2 x = - 1 + 9$

Add $- 1$ and $9$ .

$2 x = 8$

Divide each term in $2 x = 8$ by $2$ and simplify.

Divide each term in $2 x = 8$ by $2$ .

$\frac{2 x}{2} = \frac{8}{2}$

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$\frac{2 x}{2} = \frac{8}{2}$

Divide $x$ by $1$ .

$x = \frac{8}{2}$

Simplify the right side.

Divide $8$ by $2$ .

$x = 4$

Step 7

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

$(4, 3)$

Step 8

The result can be shown in multiple forms.

Point Form:

$(4, 3)$

Equation Form:

$x = 4, y = 3$

Step 9

Solve by Addition/Elimination 2x-3y=-1 y=x-1

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