Algebra Examples

$- 5 x + y = - 2$ , $- 3 x + 6 y = - 12$

Step 1

Add $5 x$ to both sides of the equation.

$y = - 2 + 5 x$

$- 3 x + 6 y = - 12$

Step 2

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

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Step 2.1

Replace all occurrences of $y$ in $- 3 x + 6 y = - 12$ with $- 2 + 5 x$ .

$- 3 x + 6 (- 2 + 5 x) = - 12$

$y = - 2 + 5 x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 3 x + 6 (- 2 + 5 x)$ .

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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.

$- 3 x + 6 \cdot - 2 + 6 (5 x) = - 12$

$y = - 2 + 5 x$

Step 2.2.1.1.2

Multiply $6$ by $- 2$ .

$- 3 x - 12 + 6 (5 x) = - 12$

$y = - 2 + 5 x$

Step 2.2.1.1.3

Multiply $5$ by $6$ .

$- 3 x - 12 + 30 x = - 12$

$y = - 2 + 5 x$

$- 3 x - 12 + 30 x = - 12$

$y = - 2 + 5 x$

Step 2.2.1.2

Add $- 3 x$ and $30 x$ .

$27 x - 12 = - 12$

$y = - 2 + 5 x$

$27 x - 12 = - 12$

$y = - 2 + 5 x$

$27 x - 12 = - 12$

$y = - 2 + 5 x$

$27 x - 12 = - 12$

$y = - 2 + 5 x$

Step 3

Solve for $x$ in $27 x - 12 = - 12$ .

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Step 3.1

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

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Step 3.1.1

Add $12$ to both sides of the equation.

$27 x = - 12 + 12$

$y = - 2 + 5 x$

Step 3.1.2

Add $- 12$ and $12$ .

$27 x = 0$

$y = - 2 + 5 x$

$27 x = 0$

$y = - 2 + 5 x$

Step 3.2

Divide each term in $27 x = 0$ by $27$ and simplify.

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Step 3.2.1

Divide each term in $27 x = 0$ by $27$ .

$\frac{27 x}{27} = \frac{0}{27}$

$y = - 2 + 5 x$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $27$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{27 x}{27} = \frac{0}{27}$

$y = - 2 + 5 x$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{0}{27}$

$y = - 2 + 5 x$

$x = \frac{0}{27}$

$y = - 2 + 5 x$

$x = \frac{0}{27}$

$y = - 2 + 5 x$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $0$ by $27$ .

$x = 0$

$y = - 2 + 5 x$

$x = 0$

$y = - 2 + 5 x$

$x = 0$

$y = - 2 + 5 x$

$x = 0$

$y = - 2 + 5 x$

Step 4

Replace all occurrences of $x$ with $0$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = - 2 + 5 x$ with $0$ .

$y = - 2 + 5 (0)$

$x = 0$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- 2 + 5 (0)$ .

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Step 4.2.1.1

Multiply $5$ by $0$ .

$y = - 2 + 0$

$x = 0$

Step 4.2.1.2

Add $- 2$ and $0$ .

$y = - 2$

$x = 0$

$y = - 2$

$x = 0$

$y = - 2$

$x = 0$

$y = - 2$

$x = 0$

Step 5

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

$(0, - 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(0, - 2)$

Equation Form:

$x = 0, y = - 2$

Step 7