Finite Math Examples

$3 x - 4 y = 12$ ,

$x + 2 y = 4$

Step 1

Subtract

$2 y$ from both sides of the equation.

$x = 4 - 2 y$

$3 x - 4 y = 12$

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

$3 x - 4 y = 12$ with

$4 - 2 y$ .

$3 (4 - 2 y) - 4 y = 12$

$x = 4 - 2 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify

$3 (4 - 2 y) - 4 y$ .

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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.

$3 \cdot 4 + 3 (- 2 y) - 4 y = 12$

$x = 4 - 2 y$

Step 2.2.1.1.2

Multiply

$3$ by

$4$ .

$12 + 3 (- 2 y) - 4 y = 12$

$x = 4 - 2 y$

Step 2.2.1.1.3

Multiply

$- 2$ by

$3$ .

$12 - 6 y - 4 y = 12$

$x = 4 - 2 y$

$12 - 6 y - 4 y = 12$

$x = 4 - 2 y$

Step 2.2.1.2

Subtract

$4 y$ from

$- 6 y$ .

$12 - 10 y = 12$

$x = 4 - 2 y$

$12 - 10 y = 12$

$x = 4 - 2 y$

$12 - 10 y = 12$

$x = 4 - 2 y$

$12 - 10 y = 12$

$x = 4 - 2 y$

Step 3

Solve for

$y$ in

$12 - 10 y = 12$ .

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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

$12$ from both sides of the equation.

$- 10 y = 12 - 12$

$x = 4 - 2 y$

Step 3.1.2

Subtract

$12$ from

$12$ .

$- 10 y = 0$

$x = 4 - 2 y$

$- 10 y = 0$

$x = 4 - 2 y$

Step 3.2

Divide each term in

$- 10 y = 0$ by

$- 10$ and simplify.

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Step 3.2.1

Divide each term in

$- 10 y = 0$ by

$- 10$ .

$\frac{- 10 y}{- 10} = \frac{0}{- 10}$

$x = 4 - 2 y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of

$- 10$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 10 y}{- 10} = \frac{0}{- 10}$

$x = 4 - 2 y$

Step 3.2.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{0}{- 10}$

$x = 4 - 2 y$

$y = \frac{0}{- 10}$

$x = 4 - 2 y$

$y = \frac{0}{- 10}$

$x = 4 - 2 y$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide

$0$ by

$- 10$ .

$y = 0$

$x = 4 - 2 y$

$y = 0$

$x = 4 - 2 y$

$y = 0$

$x = 4 - 2 y$

$y = 0$

$x = 4 - 2 y$

Step 4

Replace all occurrences of

$y$ with

$0$ in each equation.

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Step 4.1

Replace all occurrences of

$y$ in

$x = 4 - 2 y$ with

$0$ .

$x = 4 - 2 \cdot 0$

$y = 0$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify

$4 - 2 \cdot 0$ .

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Step 4.2.1.1

Multiply

$- 2$ by

$0$ .

$x = 4 + 0$

$y = 0$

Step 4.2.1.2

Add

$4$ and

$0$ .

$x = 4$

$y = 0$

$x = 4$

$y = 0$

$x = 4$

$y = 0$

$x = 4$

$y = 0$

Step 5

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

$(4, 0)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, 0)$

Equation Form:

$x = 4, y = 0$

Step 7

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$