Finite Math Examples

$- 2 x - 4 y = - 8$ , $4 x - y = 7$

Step 1

Solve for $x$ in $- 2 x - 4 y = - 8$ .

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Step 1.1

Add $4 y$ to both sides of the equation.

$- 2 x = - 8 + 4 y$

$4 x - y = 7$

Step 1.2

Divide each term in $- 2 x = - 8 + 4 y$ by $- 2$ and simplify.

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Step 1.2.1

Divide each term in $- 2 x = - 8 + 4 y$ by $- 2$ .

$\frac{- 2 x}{- 2} = \frac{- 8}{- 2} + \frac{4 y}{- 2}$

$4 x - y = 7$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $- 2$ .

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Step 1.2.2.1.1

Cancel the common factor.

$\frac{- 2 x}{- 2} = \frac{- 8}{- 2} + \frac{4 y}{- 2}$

$4 x - y = 7$

Step 1.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 8}{- 2} + \frac{4 y}{- 2}$

$4 x - y = 7$

$x = \frac{- 8}{- 2} + \frac{4 y}{- 2}$

$4 x - y = 7$

$x = \frac{- 8}{- 2} + \frac{4 y}{- 2}$

$4 x - y = 7$

Step 1.2.3

Simplify the right side.

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Step 1.2.3.1

Simplify each term.

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Step 1.2.3.1.1

Divide $- 8$ by $- 2$ .

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

$4 x - y = 7$

Step 1.2.3.1.2

Cancel the common factor of $4$ and $- 2$ .

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Step 1.2.3.1.2.1

Factor $2$ out of $4 y$ .

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

$4 x - y = 7$

Step 1.2.3.1.2.2

Move the negative one from the denominator of $\frac{2 y}{- 1}$ .

$x = 4 - 1 \cdot (2 y)$

$4 x - y = 7$

$x = 4 - 1 \cdot (2 y)$

$4 x - y = 7$

Step 1.2.3.1.3

Rewrite $- 1 \cdot (2 y)$ as $- (2 y)$ .

$x = 4 - (2 y)$

$4 x - y = 7$

Step 1.2.3.1.4

Multiply $2$ by $- 1$ .

$x = 4 - 2 y$

$4 x - y = 7$

$x = 4 - 2 y$

$4 x - y = 7$

$x = 4 - 2 y$

$4 x - y = 7$

$x = 4 - 2 y$

$4 x - y = 7$

$x = 4 - 2 y$

$4 x - y = 7$

Step 2

Replace all occurrences of $x$ with $4 - 2 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $4 x - y = 7$ with $4 - 2 y$ .

$4 (4 - 2 y) - y = 7$

$x = 4 - 2 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $4 (4 - 2 y) - y$ .

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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.

$4 \cdot 4 + 4 (- 2 y) - y = 7$

$x = 4 - 2 y$

Step 2.2.1.1.2

Multiply $4$ by $4$ .

$16 + 4 (- 2 y) - y = 7$

$x = 4 - 2 y$

Step 2.2.1.1.3

Multiply $- 2$ by $4$ .

$16 - 8 y - y = 7$

$x = 4 - 2 y$

$16 - 8 y - y = 7$

$x = 4 - 2 y$

Step 2.2.1.2

Subtract $y$ from $- 8 y$ .

$16 - 9 y = 7$

$x = 4 - 2 y$

$16 - 9 y = 7$

$x = 4 - 2 y$

$16 - 9 y = 7$

$x = 4 - 2 y$

$16 - 9 y = 7$

$x = 4 - 2 y$

Step 3

Solve for $y$ in $16 - 9 y = 7$ .

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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 $16$ from both sides of the equation.

$- 9 y = 7 - 16$

$x = 4 - 2 y$

Step 3.1.2

Subtract $16$ from $7$ .

$- 9 y = - 9$

$x = 4 - 2 y$

$- 9 y = - 9$

$x = 4 - 2 y$

Step 3.2

Divide each term in $- 9 y = - 9$ by $- 9$ and simplify.

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Step 3.2.1

Divide each term in $- 9 y = - 9$ by $- 9$ .

$\frac{- 9 y}{- 9} = \frac{- 9}{- 9}$

$x = 4 - 2 y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $- 9$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 9 y}{- 9} = \frac{- 9}{- 9}$

$x = 4 - 2 y$

Step 3.2.2.1.2

Divide $y$ by $1$ .

$y = \frac{- 9}{- 9}$

$x = 4 - 2 y$

$y = \frac{- 9}{- 9}$

$x = 4 - 2 y$

$y = \frac{- 9}{- 9}$

$x = 4 - 2 y$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $- 9$ by $- 9$ .

$y = 1$

$x = 4 - 2 y$

$y = 1$

$x = 4 - 2 y$

$y = 1$

$x = 4 - 2 y$

$y = 1$

$x = 4 - 2 y$

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 $x = 4 - 2 y$ with $1$ .

$x = 4 - 2 \cdot 1$

$y = 1$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $4 - 2 \cdot 1$ .

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Step 4.2.1.1

Multiply $- 2$ by $1$ .

$x = 4 - 2$

$y = 1$

Step 4.2.1.2

Subtract $2$ from $4$ .

$x = 2$

$y = 1$

$x = 2$

$y = 1$

$x = 2$

$y = 1$

$x = 2$

$y = 1$

Step 5

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

$(2, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(2, 1)$

Equation Form:

$x = 2, y = 1$

Step 7