Algebra Examples

$- 2 x - y = 1$ $- 6 x = 3 y + 3$

Step 1

Add $2 x$ to both sides of the equation.

$- y = 1 + 2 x$

$- 6 x = 3 y + 3$

Step 2

Divide each term in $- y = 1 + 2 x$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- y = 1 + 2 x$ by $- 1$ .

$\frac{- y}{- 1} = \frac{1}{- 1} + \frac{2 x}{- 1}$

$- 6 x = 3 y + 3$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{y}{1} = \frac{1}{- 1} + \frac{2 x}{- 1}$

$- 6 x = 3 y + 3$

Step 2.2.2

Divide $y$ by $1$ .

$y = \frac{1}{- 1} + \frac{2 x}{- 1}$

$- 6 x = 3 y + 3$

$y = \frac{1}{- 1} + \frac{2 x}{- 1}$

$- 6 x = 3 y + 3$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Divide $1$ by $- 1$ .

$y = - 1 + \frac{2 x}{- 1}$

$- 6 x = 3 y + 3$

Step 2.3.1.2

Move the negative one from the denominator of $\frac{2 x}{- 1}$ .

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

$- 6 x = 3 y + 3$

Step 2.3.1.3

Rewrite $- 1 \cdot (2 x)$ as $- (2 x)$ .

$y = - 1 - (2 x)$

$- 6 x = 3 y + 3$

Step 2.3.1.4

Multiply $2$ by $- 1$ .

$y = - 1 - 2 x$

$- 6 x = 3 y + 3$

$y = - 1 - 2 x$

$- 6 x = 3 y + 3$

$y = - 1 - 2 x$

$- 6 x = 3 y + 3$

$y = - 1 - 2 x$

$- 6 x = 3 y + 3$

Step 3

Rewrite the equation as $3 y + 3 = - 6 x$ .

$3 y + 3 = - 6 x$

$y = - 1 - 2 x$

Step 4

Subtract $3$ from both sides of the equation.

$3 y = - 6 x - 3$

$y = - 1 - 2 x$

Step 5

Divide each term in $3 y = - 6 x - 3$ by $3$ and simplify.

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Step 5.1

Divide each term in $3 y = - 6 x - 3$ by $3$ .

$\frac{3 y}{3} = \frac{- 6 x}{3} + \frac{- 3}{3}$

$y = - 1 - 2 x$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $3$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{3 y}{3} = \frac{- 6 x}{3} + \frac{- 3}{3}$

$y = - 1 - 2 x$

Step 5.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 6 x}{3} + \frac{- 3}{3}$

$y = - 1 - 2 x$

$y = \frac{- 6 x}{3} + \frac{- 3}{3}$

$y = - 1 - 2 x$

$y = \frac{- 6 x}{3} + \frac{- 3}{3}$

$y = - 1 - 2 x$

Step 5.3

Simplify the right side.

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Step 5.3.1

Simplify each term.

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Step 5.3.1.1

Cancel the common factor of $- 6$ and $3$ .

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Step 5.3.1.1.1

Factor $3$ out of $- 6 x$ .

$y = \frac{3 (- 2 x)}{3} + \frac{- 3}{3}$

$y = - 1 - 2 x$

Step 5.3.1.1.2

Cancel the common factors.

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Step 5.3.1.1.2.1

Factor $3$ out of $3$ .

$y = \frac{3 (- 2 x)}{3 (1)} + \frac{- 3}{3}$

$y = - 1 - 2 x$

Step 5.3.1.1.2.2

Cancel the common factor.

$y = \frac{3 (- 2 x)}{3 \cdot 1} + \frac{- 3}{3}$

$y = - 1 - 2 x$

Step 5.3.1.1.2.3

Rewrite the expression.

$y = \frac{- 2 x}{1} + \frac{- 3}{3}$

$y = - 1 - 2 x$

Step 5.3.1.1.2.4

Divide $- 2 x$ by $1$ .

$y = - 2 x + \frac{- 3}{3}$

$y = - 1 - 2 x$

$y = - 2 x + \frac{- 3}{3}$

$y = - 1 - 2 x$

$y = - 2 x + \frac{- 3}{3}$

$y = - 1 - 2 x$

Step 5.3.1.2

Divide $- 3$ by $3$ .

$y = - 2 x - 1$

$y = - 1 - 2 x$

$y = - 2 x - 1$

$y = - 1 - 2 x$

$y = - 2 x - 1$

$y = - 1 - 2 x$

$y = - 2 x - 1$

$y = - 1 - 2 x$

Step 6

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

Always true

Step 7