Finite Math Examples

$- \frac{1}{2} x + 4 y = - 2$ , $x - 6 y = 6$

Step 1

Add $6 y$ to both sides of the equation.

$x = 6 + 6 y$

$- \frac{1}{2} x + 4 y = - 2$

Step 2

Replace all occurrences of $x$ with $6 + 6 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $- \frac{1}{2} x + 4 y = - 2$ with $6 + 6 y$ .

$- \frac{1}{2} \cdot (6 + 6 y) + 4 y = - 2$

$x = 6 + 6 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $- \frac{1}{2} \cdot (6 + 6 y) + 4 y$ .

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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.

$- \frac{1}{2} \cdot 6 - \frac{1}{2} \cdot (6 y) + 4 y = - 2$

$x = 6 + 6 y$

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 $- \frac{1}{2}$ into the numerator.

$\frac{- 1}{2} \cdot 6 - \frac{1}{2} \cdot (6 y) + 4 y = - 2$

$x = 6 + 6 y$

Step 2.2.1.1.2.2

Factor $2$ out of $6$ .

$\frac{- 1}{2} \cdot (2 (3)) - \frac{1}{2} \cdot (6 y) + 4 y = - 2$

$x = 6 + 6 y$

Step 2.2.1.1.2.3

Cancel the common factor.

$\frac{- 1}{2} \cdot (2 \cdot 3) - \frac{1}{2} \cdot (6 y) + 4 y = - 2$

$x = 6 + 6 y$

Step 2.2.1.1.2.4

Rewrite the expression.

$- 1 \cdot 3 - \frac{1}{2} \cdot (6 y) + 4 y = - 2$

$x = 6 + 6 y$

$- 1 \cdot 3 - \frac{1}{2} \cdot (6 y) + 4 y = - 2$

$x = 6 + 6 y$

Step 2.2.1.1.3

Multiply $- 1$ by $3$ .

$- 3 - \frac{1}{2} \cdot (6 y) + 4 y = - 2$

$x = 6 + 6 y$

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 $- \frac{1}{2}$ into the numerator.

$- 3 + \frac{- 1}{2} \cdot (6 y) + 4 y = - 2$

$x = 6 + 6 y$

Step 2.2.1.1.4.2

Factor $2$ out of $6 y$ .

$- 3 + \frac{- 1}{2} \cdot (2 (3 y)) + 4 y = - 2$

$x = 6 + 6 y$

Step 2.2.1.1.4.3

Cancel the common factor.

$- 3 + \frac{- 1}{2} \cdot (2 (3 y)) + 4 y = - 2$

$x = 6 + 6 y$

Step 2.2.1.1.4.4

Rewrite the expression.

$- 3 - 1 (3 y) + 4 y = - 2$

$x = 6 + 6 y$

$- 3 - 1 (3 y) + 4 y = - 2$

$x = 6 + 6 y$

Step 2.2.1.1.5

Multiply $3$ by $- 1$ .

$- 3 - 3 y + 4 y = - 2$

$x = 6 + 6 y$

$- 3 - 3 y + 4 y = - 2$

$x = 6 + 6 y$

Step 2.2.1.2

Add $- 3 y$ and $4 y$ .

$- 3 + y = - 2$

$x = 6 + 6 y$

$- 3 + y = - 2$

$x = 6 + 6 y$

$- 3 + y = - 2$

$x = 6 + 6 y$

$- 3 + y = - 2$

$x = 6 + 6 y$

Step 3

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

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Step 3.1

Add $3$ to both sides of the equation.

$y = - 2 + 3$

$x = 6 + 6 y$

Step 3.2

Add $- 2$ and $3$ .

$y = 1$

$x = 6 + 6 y$

$y = 1$

$x = 6 + 6 y$

Step 4

Replace all occurrences of $y$ with $1$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = 6 + 6 y$ with $1$ .

$x = 6 + 6 (1)$

$y = 1$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $6 + 6 (1)$ .

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Step 4.2.1.1

Multiply $6$ by $1$ .

$x = 6 + 6$

$y = 1$

Step 4.2.1.2

Add $6$ and $6$ .

$x = 12$

$y = 1$

$x = 12$

$y = 1$

$x = 12$

$y = 1$

$x = 12$

$y = 1$

Step 5

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

$(12, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(12, 1)$

Equation Form:

$x = 12, y = 1$

Step 7