Finite Math Examples

$3 x - 9 y = 21$ , $- 2 x + 6 y = - 14$

Step 1

Solve for $x$ in $3 x - 9 y = 21$ .

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Step 1.1

Add $9 y$ to both sides of the equation.

$3 x = 21 + 9 y$

$- 2 x + 6 y = - 14$

Step 1.2

Divide each term in $3 x = 21 + 9 y$ by $3$ and simplify.

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Step 1.2.1

Divide each term in $3 x = 21 + 9 y$ by $3$ .

$\frac{3 x}{3} = \frac{21}{3} + \frac{9 y}{3}$

$- 2 x + 6 y = - 14$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $3$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{21}{3} + \frac{9 y}{3}$

$- 2 x + 6 y = - 14$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{21}{3} + \frac{9 y}{3}$

$- 2 x + 6 y = - 14$

$x = \frac{21}{3} + \frac{9 y}{3}$

$- 2 x + 6 y = - 14$

$x = \frac{21}{3} + \frac{9 y}{3}$

$- 2 x + 6 y = - 14$

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 $21$ by $3$ .

$x = 7 + \frac{9 y}{3}$

$- 2 x + 6 y = - 14$

Step 1.2.3.1.2

Cancel the common factor of $9$ and $3$ .

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Step 1.2.3.1.2.1

Factor $3$ out of $9 y$ .

$x = 7 + \frac{3 (3 y)}{3}$

$- 2 x + 6 y = - 14$

Step 1.2.3.1.2.2

Cancel the common factors.

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Step 1.2.3.1.2.2.1

Factor $3$ out of $3$ .

$x = 7 + \frac{3 (3 y)}{3 (1)}$

$- 2 x + 6 y = - 14$

Step 1.2.3.1.2.2.2

Cancel the common factor.

$x = 7 + \frac{3 (3 y)}{3 \cdot 1}$

$- 2 x + 6 y = - 14$

Step 1.2.3.1.2.2.3

Rewrite the expression.

$x = 7 + \frac{3 y}{1}$

$- 2 x + 6 y = - 14$

Step 1.2.3.1.2.2.4

Divide $3 y$ by $1$ .

$x = 7 + 3 y$

$- 2 x + 6 y = - 14$

$x = 7 + 3 y$

$- 2 x + 6 y = - 14$

$x = 7 + 3 y$

$- 2 x + 6 y = - 14$

$x = 7 + 3 y$

$- 2 x + 6 y = - 14$

$x = 7 + 3 y$

$- 2 x + 6 y = - 14$

$x = 7 + 3 y$

$- 2 x + 6 y = - 14$

$x = 7 + 3 y$

$- 2 x + 6 y = - 14$

Step 2

Replace all occurrences of $x$ with $7 + 3 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- 2 x + 6 y = - 14$ with $7 + 3 y$ .

$- 2 (7 + 3 y) + 6 y = - 14$

$x = 7 + 3 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 2 (7 + 3 y) + 6 y$ .

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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.

$- 2 \cdot 7 - 2 (3 y) + 6 y = - 14$

$x = 7 + 3 y$

Step 2.2.1.1.2

Multiply $- 2$ by $7$ .

$- 14 - 2 (3 y) + 6 y = - 14$

$x = 7 + 3 y$

Step 2.2.1.1.3

Multiply $3$ by $- 2$ .

$- 14 - 6 y + 6 y = - 14$

$x = 7 + 3 y$

$- 14 - 6 y + 6 y = - 14$

$x = 7 + 3 y$

Step 2.2.1.2

Combine the opposite terms in $- 14 - 6 y + 6 y$ .

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Step 2.2.1.2.1

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

$- 14 + 0 = - 14$

$x = 7 + 3 y$

Step 2.2.1.2.2

Add $- 14$ and $0$ .

$- 14 = - 14$

$x = 7 + 3 y$

$- 14 = - 14$

$x = 7 + 3 y$

$- 14 = - 14$

$x = 7 + 3 y$

$- 14 = - 14$

$x = 7 + 3 y$

$- 14 = - 14$

$x = 7 + 3 y$

Step 3

Remove any equations from the system that are always true.

$x = 7 + 3 y$

Step 4