Finite Math Examples

$5 x + y = 0$ , $5 x + 2 y = 30$

Step 1

Subtract $5 x$ from both sides of the equation.

$y = - 5 x$

$5 x + 2 y = 30$

Step 2

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

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Step 2.1

Replace all occurrences of $y$ in $5 x + 2 y = 30$ with $- 5 x$ .

$5 x + 2 (- 5 x) = 30$

$y = - 5 x$

Step 2.2

Simplify the left side.

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Step 2.2.1

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

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Step 2.2.1.1

Multiply $- 5$ by $2$ .

$5 x - 10 x = 30$

$y = - 5 x$

Step 2.2.1.2

Subtract $10 x$ from $5 x$ .

$- 5 x = 30$

$y = - 5 x$

$- 5 x = 30$

$y = - 5 x$

$- 5 x = 30$

$y = - 5 x$

$- 5 x = 30$

$y = - 5 x$

Step 3

Divide each term in $- 5 x = 30$ by $- 5$ and simplify.

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Step 3.1

Divide each term in $- 5 x = 30$ by $- 5$ .

$\frac{- 5 x}{- 5} = \frac{30}{- 5}$

$y = - 5 x$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $- 5$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{- 5 x}{- 5} = \frac{30}{- 5}$

$y = - 5 x$

Step 3.2.1.2

Divide $x$ by $1$ .

$x = \frac{30}{- 5}$

$y = - 5 x$

$x = \frac{30}{- 5}$

$y = - 5 x$

$x = \frac{30}{- 5}$

$y = - 5 x$

Step 3.3

Simplify the right side.

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Step 3.3.1

Divide $30$ by $- 5$ .

$x = - 6$

$y = - 5 x$

$x = - 6$

$y = - 5 x$

$x = - 6$

$y = - 5 x$

Step 4

Replace all occurrences of $x$ with $- 6$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = - 5 x$ with $- 6$ .

$y = - 5 \cdot - 6$

$x = - 6$

Step 4.2

Simplify the right side.

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Step 4.2.1

Multiply $- 5$ by $- 6$ .

$y = 30$

$x = - 6$

$y = 30$

$x = - 6$

$y = 30$

$x = - 6$

Step 5

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

$(- 6, 30)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 6, 30)$

Equation Form:

$x = - 6, y = 30$

Step 7