Algebra Examples

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

Step 1

Add $2$ to both sides of the equation.

$y = x + 2$

$- 6 y + 2 = - 4 x$

Step 2

Replace all occurrences of $y$ with $x + 2$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $- 6 y + 2 = - 4 x$ with $x + 2$ .

$- 6 (x + 2) + 2 = - 4 x$

$y = x + 2$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 6 (x + 2) + 2$ .

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Step 2.2.1.1

Simplify each term.

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Step 2.2.1.1.1

Apply the distributive property.

$- 6 x - 6 \cdot 2 + 2 = - 4 x$

$y = x + 2$

Step 2.2.1.1.2

Multiply $- 6$ by $2$ .

$- 6 x - 12 + 2 = - 4 x$

$y = x + 2$

$- 6 x - 12 + 2 = - 4 x$

$y = x + 2$

Step 2.2.1.2

Add $- 12$ and $2$ .

$- 6 x - 10 = - 4 x$

$y = x + 2$

$- 6 x - 10 = - 4 x$

$y = x + 2$

$- 6 x - 10 = - 4 x$

$y = x + 2$

$- 6 x - 10 = - 4 x$

$y = x + 2$

Step 3

Solve for $x$ in $- 6 x - 10 = - 4 x$ .

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Step 3.1

Move all terms containing $x$ to the left side of the equation.

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Step 3.1.1

Add $4 x$ to both sides of the equation.

$- 6 x - 10 + 4 x = 0$

$y = x + 2$

Step 3.1.2

Add $- 6 x$ and $4 x$ .

$- 2 x - 10 = 0$

$y = x + 2$

$- 2 x - 10 = 0$

$y = x + 2$

Step 3.2

Add $10$ to both sides of the equation.

$- 2 x = 10$

$y = x + 2$

Step 3.3

Divide each term in $- 2 x = 10$ by $- 2$ and simplify.

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Step 3.3.1

Divide each term in $- 2 x = 10$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{10}{- 2}$

$y = x + 2$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 2$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{10}{- 2}$

$y = x + 2$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{10}{- 2}$

$y = x + 2$

$x = \frac{10}{- 2}$

$y = x + 2$

$x = \frac{10}{- 2}$

$y = x + 2$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $10$ by $- 2$ .

$x = - 5$

$y = x + 2$

$x = - 5$

$y = x + 2$

$x = - 5$

$y = x + 2$

$x = - 5$

$y = x + 2$

Step 4

Replace all occurrences of $x$ with $- 5$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = x + 2$ with $- 5$ .

$y = (- 5) + 2$

$x = - 5$

Step 4.2

Simplify the right side.

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Step 4.2.1

Add $- 5$ and $2$ .

$y = - 3$

$x = - 5$

$y = - 3$

$x = - 5$

$y = - 3$

$x = - 5$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(- 5, - 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 5, - 3)$

Equation Form:

$x = - 5, y = - 3$

Step 7