Finite Math Examples

$3 x - 3 y = - 12$ , $18 x - 7 y = - 17$

Step 1

Solve for $x$ in $3 x - 3 y = - 12$ .

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Step 1.1

Add $3 y$ to both sides of the equation.

$3 x = - 12 + 3 y$

$18 x - 7 y = - 17$

Step 1.2

Divide each term in $3 x = - 12 + 3 y$ by $3$ and simplify.

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Step 1.2.1

Divide each term in $3 x = - 12 + 3 y$ by $3$ .

$\frac{3 x}{3} = \frac{- 12}{3} + \frac{3 y}{3}$

$18 x - 7 y = - 17$

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.

$\frac{3 x}{3} = \frac{- 12}{3} + \frac{3 y}{3}$

$18 x - 7 y = - 17$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 12}{3} + \frac{3 y}{3}$

$18 x - 7 y = - 17$

$x = \frac{- 12}{3} + \frac{3 y}{3}$

$18 x - 7 y = - 17$

$x = \frac{- 12}{3} + \frac{3 y}{3}$

$18 x - 7 y = - 17$

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 $- 12$ by $3$ .

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

$18 x - 7 y = - 17$

Step 1.2.3.1.2

Cancel the common factor of $3$ .

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Step 1.2.3.1.2.1

Cancel the common factor.

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

$18 x - 7 y = - 17$

Step 1.2.3.1.2.2

Divide $y$ by $1$ .

$x = - 4 + y$

$18 x - 7 y = - 17$

$x = - 4 + y$

$18 x - 7 y = - 17$

$x = - 4 + y$

$18 x - 7 y = - 17$

$x = - 4 + y$

$18 x - 7 y = - 17$

$x = - 4 + y$

$18 x - 7 y = - 17$

$x = - 4 + y$

$18 x - 7 y = - 17$

Step 2

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

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Step 2.1

Replace all occurrences of $x$ in $18 x - 7 y = - 17$ with $- 4 + y$ .

$18 (- 4 + y) - 7 y = - 17$

$x = - 4 + y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $18 (- 4 + y) - 7 y$ .

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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.

$18 \cdot - 4 + 18 y - 7 y = - 17$

$x = - 4 + y$

Step 2.2.1.1.2

Multiply $18$ by $- 4$ .

$- 72 + 18 y - 7 y = - 17$

$x = - 4 + y$

$- 72 + 18 y - 7 y = - 17$

$x = - 4 + y$

Step 2.2.1.2

Subtract $7 y$ from $18 y$ .

$- 72 + 11 y = - 17$

$x = - 4 + y$

$- 72 + 11 y = - 17$

$x = - 4 + y$

$- 72 + 11 y = - 17$

$x = - 4 + y$

$- 72 + 11 y = - 17$

$x = - 4 + y$

Step 3

Solve for $y$ in $- 72 + 11 y = - 17$ .

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Step 3.1

Move all terms not containing $y$ to the right side of the equation.

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Step 3.1.1

Add $72$ to both sides of the equation.

$11 y = - 17 + 72$

$x = - 4 + y$

Step 3.1.2

Add $- 17$ and $72$ .

$11 y = 55$

$x = - 4 + y$

$11 y = 55$

$x = - 4 + y$

Step 3.2

Divide each term in $11 y = 55$ by $11$ and simplify.

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Step 3.2.1

Divide each term in $11 y = 55$ by $11$ .

$\frac{11 y}{11} = \frac{55}{11}$

$x = - 4 + y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $11$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{11 y}{11} = \frac{55}{11}$

$x = - 4 + y$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{55}{11}$

$x = - 4 + y$

$y = \frac{55}{11}$

$x = - 4 + y$

$y = \frac{55}{11}$

$x = - 4 + y$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $55$ by $11$ .

$y = 5$

$x = - 4 + y$

$y = 5$

$x = - 4 + y$

$y = 5$

$x = - 4 + y$

$y = 5$

$x = - 4 + y$

Step 4

Replace all occurrences of $y$ with $5$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = - 4 + y$ with $5$ .

$x = - 4 + 5$

$y = 5$

Step 4.2

Simplify $x = - 4 + 5$ .

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Remove parentheses.

$x = - 4 + 5$

$y = 5$

$x = - 4 + 5$

$y = 5$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Add $- 4$ and $5$ .

$x = 1$

$y = 5$

$x = 1$

$y = 5$

$x = 1$

$y = 5$

$x = 1$

$y = 5$

Step 5

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(1, 5)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, 5)$

Equation Form:

$x = 1, y = 5$

Step 7