Finite Math Examples

$x - y = 9$ , $x + y = 6$

Add $y$ to both sides of the equation.

$x = 9 + y$

$x + y = 6$

Replace all occurrences of $x$ in $x + y = 6$ with $9 + y$ .

$x = 9 + y$

$(9 + y) + y = 6$

Add $y$ and $y$ .

$x = 9 + y$

$9 + 2 y = 6$

Solve for $y$ in the second equation.

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

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Subtract $9$ from both sides of the equation.

$x = 9 + y$

$2 y = 6 - 9$

Subtract $9$ from $6$ .

$x = 9 + y$

$2 y = - 3$

$x = 9 + y$

$2 y = - 3$

Divide each term by $2$ and simplify.

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Divide each term in $2 y = - 3$ by $2$ .

$x = 9 + y$

$\frac{2 y}{2} = \frac{- 3}{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$x = 9 + y$

$\frac{2 y}{2} = \frac{- 3}{2}$

Divide $y$ by $1$ .

$x = 9 + y$

$y = \frac{- 3}{2}$

$x = 9 + y$

$y = \frac{- 3}{2}$

Move the negative in front of the fraction.

$x = 9 + y$

$y = - \frac{3}{2}$

$x = 9 + y$

$y = - \frac{3}{2}$

$x = 9 + y$

$y = - \frac{3}{2}$

Replace all occurrences of $y$ in $x = 9 + y$ with $- \frac{3}{2}$ .

$x = 9 - \frac{3}{2}$

$y = - \frac{3}{2}$

Simplify.

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Remove parentheses.

$x = 9 - \frac{3}{2}$

$y = - \frac{3}{2}$

Simplify $9 - \frac{3}{2}$ .

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To write $9$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$x = 9 \cdot \frac{2}{2} - \frac{3}{2}$

$y = - \frac{3}{2}$

Combine $9$ and $\frac{2}{2}$ .

$x = \frac{9 \cdot 2}{2} - \frac{3}{2}$

$y = - \frac{3}{2}$

Combine the numerators over the common denominator.

$x = \frac{9 \cdot 2 - 3}{2}$

$y = - \frac{3}{2}$

Simplify the numerator.

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Multiply $9$ by $2$ .

$x = \frac{18 - 3}{2}$

$y = - \frac{3}{2}$

Subtract $3$ from $18$ .

$x = \frac{15}{2}$

$y = - \frac{3}{2}$

$x = \frac{15}{2}$

$y = - \frac{3}{2}$

$x = \frac{15}{2}$

$y = - \frac{3}{2}$

$x = \frac{15}{2}$

$y = - \frac{3}{2}$

The solution to the system of equations can be represented as a point.

$(\frac{15}{2}, - \frac{3}{2})$

The result can be shown in multiple forms.

Point Form:

$(\frac{15}{2}, - \frac{3}{2})$

Equation Form:

$x = \frac{15}{2}, y = - \frac{3}{2}$

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