Finite Math Examples

$5 x + 3 y = 30$ , $x - 3 y = 0$ , $x = 2$

Step 1

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

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Step 1.1

Replace all occurrences of $x$ in $5 x + 3 y = 30$ with $2$ .

$5 (2) + 3 y = 30$

$x = 2$

$x - 3 y = 0$

Step 1.2

Simplify the left side.

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Step 1.2.1

Multiply $5$ by $2$ .

$10 + 3 y = 30$

$x = 2$

$x - 3 y = 0$

$10 + 3 y = 30$

$x = 2$

$x - 3 y = 0$

Step 1.3

Replace all occurrences of $x$ in $x - 3 y = 0$ with $2$ .

$(2) - 3 y = 0$

$10 + 3 y = 30$

$x = 2$

Step 1.4

Simplify the left side.

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Step 1.4.1

Remove parentheses.

$2 - 3 y = 0$

$10 + 3 y = 30$

$x = 2$

$2 - 3 y = 0$

$10 + 3 y = 30$

$x = 2$

$2 - 3 y = 0$

$10 + 3 y = 30$

$x = 2$

Step 2

Solve for $y$ in $2 - 3 y = 0$ .

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Step 2.1

Subtract $2$ from both sides of the equation.

$- 3 y = - 2$

$10 + 3 y = 30$

$x = 2$

Step 2.2

Divide each term in $- 3 y = - 2$ by $- 3$ and simplify.

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Step 2.2.1

Divide each term in $- 3 y = - 2$ by $- 3$ .

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

$10 + 3 y = 30$

$x = 2$

Step 2.2.2

Simplify the left side.

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Step 2.2.2.1

Cancel the common factor of $- 3$ .

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Step 2.2.2.1.1

Cancel the common factor.

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

$10 + 3 y = 30$

$x = 2$

Step 2.2.2.1.2

Divide $y$ by $1$ .

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

$10 + 3 y = 30$

$x = 2$

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

$10 + 3 y = 30$

$x = 2$

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

$10 + 3 y = 30$

$x = 2$

Step 2.2.3

Simplify the right side.

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Step 2.2.3.1

Dividing two negative values results in a positive value.

$y = \frac{2}{3}$

$10 + 3 y = 30$

$x = 2$

$y = \frac{2}{3}$

$10 + 3 y = 30$

$x = 2$

$y = \frac{2}{3}$

$10 + 3 y = 30$

$x = 2$

$y = \frac{2}{3}$

$10 + 3 y = 30$

$x = 2$

Step 3

Replace all occurrences of $y$ with $\frac{2}{3}$ in each equation.

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Step 3.1

Replace all occurrences of $y$ in $10 + 3 y = 30$ with $\frac{2}{3}$ .

$10 + 3 (\frac{2}{3}) = 30$

$y = \frac{2}{3}$

$x = 2$

Step 3.2

Simplify the left side.

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Step 3.2.1

Simplify $10 + 3 (\frac{2}{3})$ .

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Step 3.2.1.1

Cancel the common factor of $3$ .

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Step 3.2.1.1.1

Cancel the common factor.

$10 + 3 (\frac{2}{3}) = 30$

$y = \frac{2}{3}$

$x = 2$

Step 3.2.1.1.2

Rewrite the expression.

$10 + 2 = 30$

$y = \frac{2}{3}$

$x = 2$

$10 + 2 = 30$

$y = \frac{2}{3}$

$x = 2$

Step 3.2.1.2

Add $10$ and $2$ .

$12 = 30$

$y = \frac{2}{3}$

$x = 2$

$12 = 30$

$y = \frac{2}{3}$

$x = 2$

$12 = 30$

$y = \frac{2}{3}$

$x = 2$

$12 = 30$

$y = \frac{2}{3}$

$x = 2$

Step 4

Since $12 = 30$ is not true, there is no solution.

No solution

Step 5