Finite Math Examples

$5 x + 15 y = 20$ , $2 x + 6 y = 8$

Step 1

Solve for $x$ in $5 x + 15 y = 20$ .

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Step 1.1

Subtract $15 y$ from both sides of the equation.

$5 x = 20 - 15 y$

$2 x + 6 y = 8$

Step 1.2

Divide each term in $5 x = 20 - 15 y$ by $5$ and simplify.

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Step 1.2.1

Divide each term in $5 x = 20 - 15 y$ by $5$ .

$\frac{5 x}{5} = \frac{20}{5} + \frac{- 15 y}{5}$

$2 x + 6 y = 8$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $5$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{20}{5} + \frac{- 15 y}{5}$

$2 x + 6 y = 8$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{20}{5} + \frac{- 15 y}{5}$

$2 x + 6 y = 8$

$x = \frac{20}{5} + \frac{- 15 y}{5}$

$2 x + 6 y = 8$

$x = \frac{20}{5} + \frac{- 15 y}{5}$

$2 x + 6 y = 8$

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

Divide $20$ by $5$ .

$x = 4 + \frac{- 15 y}{5}$

$2 x + 6 y = 8$

Step 1.2.3.1.2

Cancel the common factor of $- 15$ and $5$ .

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Step 1.2.3.1.2.1

Factor $5$ out of $- 15 y$ .

$x = 4 + \frac{5 (- 3 y)}{5}$

$2 x + 6 y = 8$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $5$ out of $5$ .

$x = 4 + \frac{5 (- 3 y)}{5 (1)}$

$2 x + 6 y = 8$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$x = 4 + \frac{5 (- 3 y)}{5 \cdot 1}$

$2 x + 6 y = 8$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$x = 4 + \frac{- 3 y}{1}$

$2 x + 6 y = 8$

Step 1.2.3.1.2.2.4

Divide $- 3 y$ by $1$ .

$x = 4 - 3 y$

$2 x + 6 y = 8$

$x = 4 - 3 y$

$2 x + 6 y = 8$

$x = 4 - 3 y$

$2 x + 6 y = 8$

$x = 4 - 3 y$

$2 x + 6 y = 8$

$x = 4 - 3 y$

$2 x + 6 y = 8$

$x = 4 - 3 y$

$2 x + 6 y = 8$

$x = 4 - 3 y$

$2 x + 6 y = 8$

Step 2

Replace all occurrences of $x$ with $4 - 3 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $2 x + 6 y = 8$ with $4 - 3 y$ .

$2 (4 - 3 y) + 6 y = 8$

$x = 4 - 3 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $2 (4 - 3 y) + 6 y$ .

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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.

$2 \cdot 4 + 2 (- 3 y) + 6 y = 8$

$x = 4 - 3 y$

Step 2.2.1.1.2

Multiply $2$ by $4$ .

$8 + 2 (- 3 y) + 6 y = 8$

$x = 4 - 3 y$

Step 2.2.1.1.3

Multiply $- 3$ by $2$ .

$8 - 6 y + 6 y = 8$

$x = 4 - 3 y$

$8 - 6 y + 6 y = 8$

$x = 4 - 3 y$

Step 2.2.1.2

Combine the opposite terms in $8 - 6 y + 6 y$ .

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Step 2.2.1.2.1

Add $- 6 y$ and $6 y$ .

$8 + 0 = 8$

$x = 4 - 3 y$

Step 2.2.1.2.2

Add $8$ and $0$ .

$8 = 8$

$x = 4 - 3 y$

$8 = 8$

$x = 4 - 3 y$

$8 = 8$

$x = 4 - 3 y$

$8 = 8$

$x = 4 - 3 y$

$8 = 8$

$x = 4 - 3 y$

Step 3

Remove any equations from the system that are always true.

$x = 4 - 3 y$

Step 4

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$