Precalculus Examples

$40 x + 20 y = 21$ , $0$

Step 1

Subtract $20 y$ from both sides of the equation.

$40 x = 21 - 20 y$

Step 2

Divide each term in $40 x = 21 - 20 y$ by $40$ and simplify.

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Step 2.1

Divide each term in $40 x = 21 - 20 y$ by $40$ .

$\frac{40 x}{40} = \frac{21}{40} + \frac{- 20 y}{40}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $40$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{40 x}{40} = \frac{21}{40} + \frac{- 20 y}{40}$

Step 2.2.1.2

Divide $x$ by $1$ .

$x = \frac{21}{40} + \frac{- 20 y}{40}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Cancel the common factor of $- 20$ and $40$ .

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Step 2.3.1.1.1

Factor $20$ out of $- 20 y$ .

$x = \frac{21}{40} + \frac{20 (- y)}{40}$

Step 2.3.1.1.2

Cancel the common factors.

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Step 2.3.1.1.2.1

Factor $20$ out of $40$ .

$x = \frac{21}{40} + \frac{20 (- y)}{20 (2)}$

Step 2.3.1.1.2.2

Cancel the common factor.

$x = \frac{21}{40} + \frac{20 (- y)}{20 \cdot 2}$

Step 2.3.1.1.2.3

Rewrite the expression.

$x = \frac{21}{40} + \frac{- y}{2}$

Step 2.3.1.2

Move the negative in front of the fraction.

$x = \frac{21}{40} - \frac{y}{2}$

Step 3

Replace the variable $x$ with $\frac{21}{40} - \frac{y}{2}$ in the expression.

$0$