Finite Math Examples

$6 y + 2 x = 3$ , $6 y = 7 - x$

Step 1

Divide each term in $6 y = 7 - x$ by $6$ and simplify.

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Step 1.1

Divide each term in $6 y = 7 - x$ by $6$ .

$\frac{6 y}{6} = \frac{7}{6} + \frac{- x}{6}$

$6 y + 2 x = 3$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $6$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{6 y}{6} = \frac{7}{6} + \frac{- x}{6}$

$6 y + 2 x = 3$

Step 1.2.1.2

Divide $y$ by $1$ .

$y = \frac{7}{6} + \frac{- x}{6}$

$6 y + 2 x = 3$

$y = \frac{7}{6} + \frac{- x}{6}$

$6 y + 2 x = 3$

$y = \frac{7}{6} + \frac{- x}{6}$

$6 y + 2 x = 3$

Step 1.3

Simplify the right side.

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Step 1.3.1

Move the negative in front of the fraction.

$y = \frac{7}{6} - \frac{x}{6}$

$6 y + 2 x = 3$

$y = \frac{7}{6} - \frac{x}{6}$

$6 y + 2 x = 3$

$y = \frac{7}{6} - \frac{x}{6}$

$6 y + 2 x = 3$

Step 2

Replace all occurrences of $y$ with $\frac{7}{6} - \frac{x}{6}$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $6 y + 2 x = 3$ with $\frac{7}{6} - \frac{x}{6}$ .

$6 (\frac{7}{6} - \frac{x}{6}) + 2 x = 3$

$y = \frac{7}{6} - \frac{x}{6}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $6 (\frac{7}{6} - \frac{x}{6}) + 2 x$ .

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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.

$6 (\frac{7}{6}) + 6 (- \frac{x}{6}) + 2 x = 3$

$y = \frac{7}{6} - \frac{x}{6}$

Step 2.2.1.1.2

Cancel the common factor of $6$ .

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Step 2.2.1.1.2.1

Cancel the common factor.

$6 (\frac{7}{6}) + 6 (- \frac{x}{6}) + 2 x = 3$

$y = \frac{7}{6} - \frac{x}{6}$

Step 2.2.1.1.2.2

Rewrite the expression.

$7 + 6 (- \frac{x}{6}) + 2 x = 3$

$y = \frac{7}{6} - \frac{x}{6}$

$7 + 6 (- \frac{x}{6}) + 2 x = 3$

$y = \frac{7}{6} - \frac{x}{6}$

Step 2.2.1.1.3

Cancel the common factor of $6$ .

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Step 2.2.1.1.3.1

Move the leading negative in $- \frac{x}{6}$ into the numerator.

$7 + 6 (\frac{- x}{6}) + 2 x = 3$

$y = \frac{7}{6} - \frac{x}{6}$

Step 2.2.1.1.3.2

Cancel the common factor.

$7 + 6 (\frac{- x}{6}) + 2 x = 3$

$y = \frac{7}{6} - \frac{x}{6}$

Step 2.2.1.1.3.3

Rewrite the expression.

$7 - x + 2 x = 3$

$y = \frac{7}{6} - \frac{x}{6}$

$7 - x + 2 x = 3$

$y = \frac{7}{6} - \frac{x}{6}$

$7 - x + 2 x = 3$

$y = \frac{7}{6} - \frac{x}{6}$

Step 2.2.1.2

Add $- x$ and $2 x$ .

$7 + x = 3$

$y = \frac{7}{6} - \frac{x}{6}$

$7 + x = 3$

$y = \frac{7}{6} - \frac{x}{6}$

$7 + x = 3$

$y = \frac{7}{6} - \frac{x}{6}$

$7 + x = 3$

$y = \frac{7}{6} - \frac{x}{6}$

Step 3

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

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Step 3.1

Subtract $7$ from both sides of the equation.

$x = 3 - 7$

$y = \frac{7}{6} - \frac{x}{6}$

Step 3.2

Subtract $7$ from $3$ .

$x = - 4$

$y = \frac{7}{6} - \frac{x}{6}$

$x = - 4$

$y = \frac{7}{6} - \frac{x}{6}$

Step 4

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

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Step 4.1

Replace all occurrences of $x$ in $y = \frac{7}{6} - \frac{x}{6}$ with $- 4$ .

$y = \frac{7}{6} - \frac{- 4}{6}$

$x = - 4$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{7}{6} - \frac{- 4}{6}$ .

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Step 4.2.1.1

Combine the numerators over the common denominator.

$y = \frac{7 + 4}{6}$

$x = - 4$

Step 4.2.1.2

Add $7$ and $4$ .

$y = \frac{11}{6}$

$x = - 4$

$y = \frac{11}{6}$

$x = - 4$

$y = \frac{11}{6}$

$x = - 4$

$y = \frac{11}{6}$

$x = - 4$

Step 5

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

$(- 4, \frac{11}{6})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 4, \frac{11}{6})$

Equation Form:

$x = - 4, y = \frac{11}{6}$

Step 7