Algebra Examples

$y = 3 x - 2$ , $y = x$

Step 1

Move all terms containing variables to the left.

Tap for more steps...

Step 1.1

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

$y - 3 x = - 2, y = x$

Step 1.2

Subtract $x$ from both sides of the equation.

$y - 3 x = - 2, y - x = 0$

Step 2

Reorder the polynomial.

$- 3 x + y = - 2$

$y - x = 0$

Step 3

Reorder the polynomial.

$- x + y = 0$

$- 3 x + y = - 2$

Step 4

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

$- 3 x + y = - 2$

$(- 1) \cdot (- x + y) = (- 1) (0)$

Step 5

Simplify.

Tap for more steps...

Step 5.1

Simplify the left side.

Tap for more steps...

Step 5.1.1

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

Tap for more steps...

Step 5.1.1.1

Apply the distributive property.

$- 3 x + y = - 2$

$- 1 (- x) - 1 y = (- 1) (0)$

Step 5.1.1.2

Multiply $- 1 (- x)$ .

Tap for more steps...

Step 5.1.1.2.1

Multiply $- 1$ by $- 1$ .

$- 3 x + y = - 2$

$1 x - 1 y = (- 1) (0)$

Step 5.1.1.2.2

Multiply $x$ by $1$ .

$- 3 x + y = - 2$

$x - 1 y = (- 1) (0)$

$- 3 x + y = - 2$

$x - 1 y = (- 1) (0)$

Step 5.1.1.3

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

$- 3 x + y = - 2$

$x - y = (- 1) (0)$

$- 3 x + y = - 2$

$x - y = (- 1) (0)$

$- 3 x + y = - 2$

$x - y = (- 1) (0)$

Step 5.2

Simplify the right side.

Tap for more steps...

Step 5.2.1

Multiply $- 1$ by $0$ .

$- 3 x + y = - 2$

$x - y = 0$

$- 3 x + y = - 2$

$x - y = 0$

$- 3 x + y = - 2$

$x - y = 0$

Step 6

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

	$-$	$3$	$x$	$+$	$y$	$=$	$-$	$2$
$+$			$x$	$-$	$y$	$=$		$0$
	$-$	$2$	$x$			$=$	$-$	$2$

Step 7

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

Tap for more steps...

Step 7.1

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

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

Step 7.2

Simplify the left side.

Tap for more steps...

Step 7.2.1

Cancel the common factor of $- 2$ .

Tap for more steps...

Step 7.2.1.1

Cancel the common factor.

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

Step 7.2.1.2

Divide $x$ by $1$ .

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

Step 7.3

Simplify the right side.

Tap for more steps...

Step 7.3.1

Divide $- 2$ by $- 2$ .

$x = 1$

Step 8

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

Tap for more steps...

Step 8.1

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

$- 3 \cdot 1 + y = - 2$

Step 8.2

Multiply $- 3$ by $1$ .

$- 3 + y = - 2$

Step 8.3

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

Tap for more steps...

Step 8.3.1

Add $3$ to both sides of the equation.

$y = - 2 + 3$

Step 8.3.2

Add $- 2$ and $3$ .

$y = 1$

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

	$-$	$3$	$x$	$+$	$y$	$=$	$-$	$2$
$+$			$x$	$-$	$y$	$=$		$0$
	$-$	$2$	$x$			$=$	$-$	$2$

	$-$	$3$	$x$	$+$	$y$	$=$	$-$	$2$
$+$			$x$	$-$	$y$	$=$		$0$
	$-$	$2$	$x$			$=$	$-$	$2$

	$-$	$3$	$x$	$+$	$y$	$=$	$-$	$2$
$+$			$x$	$-$	$y$	$=$		$0$
	$-$	$2$	$x$			$=$	$-$	$2$