Finite Math Examples

$2 x = - 7 y - 13$ , $- 6 x - 5 y = - 9$

Step 1

Divide each term in $2 x = - 7 y - 13$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 x = - 7 y - 13$ by $2$ .

$\frac{2 x}{2} = \frac{- 7 y}{2} + \frac{- 13}{2}$

$- 6 x - 5 y = - 9$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor of $2$ .

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Step 1.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{- 7 y}{2} + \frac{- 13}{2}$

$- 6 x - 5 y = - 9$

Step 1.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 7 y}{2} + \frac{- 13}{2}$

$- 6 x - 5 y = - 9$

$x = \frac{- 7 y}{2} + \frac{- 13}{2}$

$- 6 x - 5 y = - 9$

$x = \frac{- 7 y}{2} + \frac{- 13}{2}$

$- 6 x - 5 y = - 9$

Step 1.3

Simplify the right side.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Move the negative in front of the fraction.

$x = - \frac{7 y}{2} + \frac{- 13}{2}$

$- 6 x - 5 y = - 9$

Step 1.3.1.2

Move the negative in front of the fraction.

$x = - \frac{7 y}{2} - \frac{13}{2}$

$- 6 x - 5 y = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

$- 6 x - 5 y = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

$- 6 x - 5 y = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

$- 6 x - 5 y = - 9$

Step 2

Replace all occurrences of $x$ with $- \frac{7 y}{2} - \frac{13}{2}$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- 6 x - 5 y = - 9$ with $- \frac{7 y}{2} - \frac{13}{2}$ .

$- 6 (- \frac{7 y}{2} - \frac{13}{2}) - 5 y = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- 6 (- \frac{7 y}{2} - \frac{13}{2}) - 5 y$ .

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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.

$- 6 (- \frac{7 y}{2}) - 6 (- \frac{13}{2}) - 5 y = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

Step 2.2.1.1.2

Cancel the common factor of $2$ .

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Step 2.2.1.1.2.1

Move the leading negative in $- \frac{7 y}{2}$ into the numerator.

$- 6 \frac{- 7 y}{2} - 6 (- \frac{13}{2}) - 5 y = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

Step 2.2.1.1.2.2

Factor $2$ out of $- 6$ .

$2 (- 3) (\frac{- 7 y}{2}) - 6 (- \frac{13}{2}) - 5 y = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

Step 2.2.1.1.2.3

Cancel the common factor.

$2 \cdot (- 3 \frac{- 7 y}{2}) - 6 (- \frac{13}{2}) - 5 y = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

Step 2.2.1.1.2.4

Rewrite the expression.

$- 3 (- 7 y) - 6 (- \frac{13}{2}) - 5 y = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

$- 3 (- 7 y) - 6 (- \frac{13}{2}) - 5 y = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

Step 2.2.1.1.3

Multiply $- 7$ by $- 3$ .

$21 y - 6 (- \frac{13}{2}) - 5 y = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

Step 2.2.1.1.4

Cancel the common factor of $2$ .

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Step 2.2.1.1.4.1

Move the leading negative in $- \frac{13}{2}$ into the numerator.

$21 y - 6 (\frac{- 13}{2}) - 5 y = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

Step 2.2.1.1.4.2

Factor $2$ out of $- 6$ .

$21 y + 2 (- 3) (\frac{- 13}{2}) - 5 y = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

Step 2.2.1.1.4.3

Cancel the common factor.

$21 y + 2 \cdot (- 3 (\frac{- 13}{2})) - 5 y = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

Step 2.2.1.1.4.4

Rewrite the expression.

$21 y - 3 \cdot - 13 - 5 y = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

$21 y - 3 \cdot - 13 - 5 y = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

Step 2.2.1.1.5

Multiply $- 3$ by $- 13$ .

$21 y + 39 - 5 y = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

$21 y + 39 - 5 y = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

Step 2.2.1.2

Subtract $5 y$ from $21 y$ .

$16 y + 39 = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

$16 y + 39 = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

$16 y + 39 = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

$16 y + 39 = - 9$

$x = - \frac{7 y}{2} - \frac{13}{2}$

Step 3

Solve for $y$ in $16 y + 39 = - 9$ .

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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

Subtract $39$ from both sides of the equation.

$16 y = - 9 - 39$

$x = - \frac{7 y}{2} - \frac{13}{2}$

Step 3.1.2

Subtract $39$ from $- 9$ .

$16 y = - 48$

$x = - \frac{7 y}{2} - \frac{13}{2}$

$16 y = - 48$

$x = - \frac{7 y}{2} - \frac{13}{2}$

Step 3.2

Divide each term in $16 y = - 48$ by $16$ and simplify.

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Step 3.2.1

Divide each term in $16 y = - 48$ by $16$ .

$\frac{16 y}{16} = \frac{- 48}{16}$

$x = - \frac{7 y}{2} - \frac{13}{2}$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $16$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{16 y}{16} = \frac{- 48}{16}$

$x = - \frac{7 y}{2} - \frac{13}{2}$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 48}{16}$

$x = - \frac{7 y}{2} - \frac{13}{2}$

$y = \frac{- 48}{16}$

$x = - \frac{7 y}{2} - \frac{13}{2}$

$y = \frac{- 48}{16}$

$x = - \frac{7 y}{2} - \frac{13}{2}$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $- 48$ by $16$ .

$y = - 3$

$x = - \frac{7 y}{2} - \frac{13}{2}$

$y = - 3$

$x = - \frac{7 y}{2} - \frac{13}{2}$

$y = - 3$

$x = - \frac{7 y}{2} - \frac{13}{2}$

$y = - 3$

$x = - \frac{7 y}{2} - \frac{13}{2}$

Step 4

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

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Step 4.1

Replace all occurrences of $y$ in $x = - \frac{7 y}{2} - \frac{13}{2}$ with $- 3$ .

$x = - \frac{7 (- 3)}{2} - \frac{13}{2}$

$y = - 3$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- \frac{7 (- 3)}{2} - \frac{13}{2}$ .

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Step 4.2.1.1

Combine the numerators over the common denominator.

$x = \frac{- 7 \cdot - 3 - 13}{2}$

$y = - 3$

Step 4.2.1.2

Simplify the expression.

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Step 4.2.1.2.1

Multiply $- 7$ by $- 3$ .

$x = \frac{21 - 13}{2}$

$y = - 3$

Step 4.2.1.2.2

Subtract $13$ from $21$ .

$x = \frac{8}{2}$

$y = - 3$

Step 4.2.1.2.3

Divide $8$ by $2$ .

$x = 4$

$y = - 3$

$x = 4$

$y = - 3$

$x = 4$

$y = - 3$

$x = 4$

$y = - 3$

$x = 4$

$y = - 3$

Step 5

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

$(4, - 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, - 3)$

Equation Form:

$x = 4, y = - 3$

Step 7