Finite Math Examples

$400 x + 460 y = 400$

Step 1

Solve for $y$ .

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Step 1.1

Subtract $400 x$ from both sides of the equation.

$460 y = 400 - 400 x$

Step 1.2

Divide each term in $460 y = 400 - 400 x$ by $460$ and simplify.

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Step 1.2.1

Divide each term in $460 y = 400 - 400 x$ by $460$ .

$\frac{460 y}{460} = \frac{400}{460} + \frac{- 400 x}{460}$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $460$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{460 y}{460} = \frac{400}{460} + \frac{- 400 x}{460}$

Step 1.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{400}{460} + \frac{- 400 x}{460}$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Cancel the common factor of $400$ and $460$ .

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Step 1.2.3.1.1.1

Factor $20$ out of $400$ .

$y = \frac{20 (20)}{460} + \frac{- 400 x}{460}$

Step 1.2.3.1.1.2

Cancel the common factors.

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Step 1.2.3.1.1.2.1

Factor $20$ out of $460$ .

$y = \frac{20 \cdot 20}{20 \cdot 23} + \frac{- 400 x}{460}$

Step 1.2.3.1.1.2.2

Cancel the common factor.

$y = \frac{20 \cdot 20}{20 \cdot 23} + \frac{- 400 x}{460}$

Step 1.2.3.1.1.2.3

Rewrite the expression.

$y = \frac{20}{23} + \frac{- 400 x}{460}$

Step 1.2.3.1.2

Cancel the common factor of $- 400$ and $460$ .

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Step 1.2.3.1.2.1

Factor $20$ out of $- 400 x$ .

$y = \frac{20}{23} + \frac{20 (- 20 x)}{460}$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $20$ out of $460$ .

$y = \frac{20}{23} + \frac{20 (- 20 x)}{20 (23)}$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$y = \frac{20}{23} + \frac{20 (- 20 x)}{20 \cdot 23}$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$y = \frac{20}{23} + \frac{- 20 x}{23}$

Step 1.2.3.1.3

Move the negative in front of the fraction.

$y = \frac{20}{23} - \frac{20 x}{23}$

Step 2

Set $400$ equal to $0$ .

$\frac{20}{23} - \frac{20 x}{23} = 0$

Step 3

Solve for $x$ .

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Step 3.1

Subtract $\frac{20}{23}$ from both sides of the equation.

$- \frac{20 x}{23} = - \frac{20}{23}$

Step 3.2

Since the expression on each side of the equation has the same denominator, the numerators must be equal.

$- 20 x = - 20$

Step 3.3

Divide each term in $- 20 x = - 20$ by $- 20$ and simplify.

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Step 3.3.1

Divide each term in $- 20 x = - 20$ by $- 20$ .

$\frac{- 20 x}{- 20} = \frac{- 20}{- 20}$

Step 3.3.2

Simplify the left side.

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Step 3.3.2.1

Cancel the common factor of $- 20$ .

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Step 3.3.2.1.1

Cancel the common factor.

$\frac{- 20 x}{- 20} = \frac{- 20}{- 20}$

Step 3.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 20}{- 20}$

Step 3.3.3

Simplify the right side.

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Step 3.3.3.1

Divide $- 20$ by $- 20$ .

$x = 1$

Step 4