Finite Math Examples

$\frac{x}{2} + \frac{y}{2} = 6$ , $x - y = - 2$

Step 1

Add $y$ to both sides of the equation.

$x = - 2 + y$

$\frac{x}{2} + \frac{y}{2} = 6$

Step 2

Replace all occurrences of $x$ with $- 2 + y$ in each equation.

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Step 2.1

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

$\frac{- 2 + y}{2} + \frac{y}{2} = 6$

$x = - 2 + y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $\frac{- 2 + y}{2} + \frac{y}{2}$ .

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Step 2.2.1.1

Combine the numerators over the common denominator.

$\frac{- 2 + y + y}{2} = 6$

$x = - 2 + y$

Step 2.2.1.2

Add $y$ and $y$ .

$\frac{- 2 + 2 y}{2} = 6$

$x = - 2 + y$

Step 2.2.1.3

Cancel the common factor of $- 2 + 2 y$ and $2$ .

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Step 2.2.1.3.1

Factor $2$ out of $- 2$ .

$\frac{2 \cdot - 1 + 2 y}{2} = 6$

$x = - 2 + y$

Step 2.2.1.3.2

Factor $2$ out of $2 y$ .

$\frac{2 \cdot - 1 + 2 (y)}{2} = 6$

$x = - 2 + y$

Step 2.2.1.3.3

Factor $2$ out of $2 (- 1) + 2 (y)$ .

$\frac{2 (- 1 + y)}{2} = 6$

$x = - 2 + y$

Step 2.2.1.3.4

Cancel the common factors.

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Step 2.2.1.3.4.1

Factor $2$ out of $2$ .

$\frac{2 (- 1 + y)}{2 (1)} = 6$

$x = - 2 + y$

Step 2.2.1.3.4.2

Cancel the common factor.

$\frac{2 (- 1 + y)}{2 \cdot 1} = 6$

$x = - 2 + y$

Step 2.2.1.3.4.3

Rewrite the expression.

$\frac{- 1 + y}{1} = 6$

$x = - 2 + y$

Step 2.2.1.3.4.4

Divide $- 1 + y$ by $1$ .

$- 1 + y = 6$

$x = - 2 + y$

$- 1 + y = 6$

$x = - 2 + y$

$- 1 + y = 6$

$x = - 2 + y$

$- 1 + y = 6$

$x = - 2 + y$

$- 1 + y = 6$

$x = - 2 + y$

$- 1 + y = 6$

$x = - 2 + y$

Step 3

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

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Step 3.1

Add $1$ to both sides of the equation.

$y = 6 + 1$

$x = - 2 + y$

Step 3.2

Add $6$ and $1$ .

$y = 7$

$x = - 2 + y$

$y = 7$

$x = - 2 + y$

Step 4

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

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Step 4.1

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

$x = - 2 + 7$

$y = 7$

Step 4.2

Simplify $x = - 2 + 7$ .

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Step 4.2.1

Simplify the left side.

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Step 4.2.1.1

Remove parentheses.

$x = - 2 + 7$

$y = 7$

$x = - 2 + 7$

$y = 7$

Step 4.2.2

Simplify the right side.

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Step 4.2.2.1

Add $- 2$ and $7$ .

$x = 5$

$y = 7$

$x = 5$

$y = 7$

$x = 5$

$y = 7$

$x = 5$

$y = 7$

Step 5

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

$(5, 7)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(5, 7)$

Equation Form:

$x = 5, y = 7$

Step 7