Finite Math Examples

$3 x + y = - 32$ , $3 x - y = - 4$

Step 1

Subtract $3 x$ from both sides of the equation.

$y = - 32 - 3 x$

$3 x - y = - 4$

Step 2

Replace all occurrences of $y$ with $- 32 - 3 x$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $3 x - y = - 4$ with $- 32 - 3 x$ .

$3 x - (- 32 - 3 x) = - 4$

$y = - 32 - 3 x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $3 x - (- 32 - 3 x)$ .

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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.

$3 x + 32 - (- 3 x) = - 4$

$y = - 32 - 3 x$

Step 2.2.1.1.2

Multiply $- 1$ by $- 32$ .

$3 x + 32 - (- 3 x) = - 4$

$y = - 32 - 3 x$

Step 2.2.1.1.3

Multiply $- 3$ by $- 1$ .

$3 x + 32 + 3 x = - 4$

$y = - 32 - 3 x$

$3 x + 32 + 3 x = - 4$

$y = - 32 - 3 x$

Step 2.2.1.2

Add $3 x$ and $3 x$ .

$6 x + 32 = - 4$

$y = - 32 - 3 x$

$6 x + 32 = - 4$

$y = - 32 - 3 x$

$6 x + 32 = - 4$

$y = - 32 - 3 x$

$6 x + 32 = - 4$

$y = - 32 - 3 x$

Step 3

Solve for $x$ in $6 x + 32 = - 4$ .

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Step 3.1

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

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Step 3.1.1

Subtract $32$ from both sides of the equation.

$6 x = - 4 - 32$

$y = - 32 - 3 x$

Step 3.1.2

Subtract $32$ from $- 4$ .

$6 x = - 36$

$y = - 32 - 3 x$

$6 x = - 36$

$y = - 32 - 3 x$

Step 3.2

Divide each term in $6 x = - 36$ by $6$ and simplify.

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Step 3.2.1

Divide each term in $6 x = - 36$ by $6$ .

$\frac{6 x}{6} = \frac{- 36}{6}$

$y = - 32 - 3 x$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of $6$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{6 x}{6} = \frac{- 36}{6}$

$y = - 32 - 3 x$

Step 3.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{- 36}{6}$

$y = - 32 - 3 x$

$x = \frac{- 36}{6}$

$y = - 32 - 3 x$

$x = \frac{- 36}{6}$

$y = - 32 - 3 x$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide $- 36$ by $6$ .

$x = - 6$

$y = - 32 - 3 x$

$x = - 6$

$y = - 32 - 3 x$

$x = - 6$

$y = - 32 - 3 x$

$x = - 6$

$y = - 32 - 3 x$

Step 4

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

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Step 4.1

Replace all occurrences of $x$ in $y = - 32 - 3 x$ with $- 6$ .

$y = - 32 - 3 \cdot - 6$

$x = - 6$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $- 32 - 3 \cdot - 6$ .

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Step 4.2.1.1

Multiply $- 3$ by $- 6$ .

$y = - 32 + 18$

$x = - 6$

Step 4.2.1.2

Add $- 32$ and $18$ .

$y = - 14$

$x = - 6$

$y = - 14$

$x = - 6$

$y = - 14$

$x = - 6$

$y = - 14$

$x = - 6$

Step 5

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

$(- 6, - 14)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(- 6, - 14)$

Equation Form:

$x = - 6, y = - 14$

Step 7