Finite Math Examples

$2 x + 3 y = 30$ ,

$2 x + y = 26$

Step 1

Subtract

$2 x$ from both sides of the equation.

$y = 26 - 2 x$

$2 x + 3 y = 30$

Step 2

Replace all occurrences of

$y$ with

$26 - 2 x$ in each equation.

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Step 2.1

Replace all occurrences of

$y$ in

$2 x + 3 y = 30$ with

$26 - 2 x$ .

$2 x + 3 (26 - 2 x) = 30$

$y = 26 - 2 x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify

$2 x + 3 (26 - 2 x)$ .

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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.

$2 x + 3 \cdot 26 + 3 (- 2 x) = 30$

$y = 26 - 2 x$

Step 2.2.1.1.2

Multiply

$3$ by

$26$ .

$2 x + 78 + 3 (- 2 x) = 30$

$y = 26 - 2 x$

Step 2.2.1.1.3

Multiply

$- 2$ by

$3$ .

$2 x + 78 - 6 x = 30$

$y = 26 - 2 x$

$2 x + 78 - 6 x = 30$

$y = 26 - 2 x$

Step 2.2.1.2

Subtract

$6 x$ from

$2 x$ .

$- 4 x + 78 = 30$

$y = 26 - 2 x$

$- 4 x + 78 = 30$

$y = 26 - 2 x$

$- 4 x + 78 = 30$

$y = 26 - 2 x$

$- 4 x + 78 = 30$

$y = 26 - 2 x$

Step 3

Solve for

$x$ in

$- 4 x + 78 = 30$ .

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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

$78$ from both sides of the equation.

$- 4 x = 30 - 78$

$y = 26 - 2 x$

Step 3.1.2

Subtract

$78$ from

$30$ .

$- 4 x = - 48$

$y = 26 - 2 x$

$- 4 x = - 48$

$y = 26 - 2 x$

Step 3.2

Divide each term in

$- 4 x = - 48$ by

$- 4$ and simplify.

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Step 3.2.1

Divide each term in

$- 4 x = - 48$ by

$- 4$ .

$\frac{- 4 x}{- 4} = \frac{- 48}{- 4}$

$y = 26 - 2 x$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of

$- 4$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 4 x}{- 4} = \frac{- 48}{- 4}$

$y = 26 - 2 x$

Step 3.2.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{- 48}{- 4}$

$y = 26 - 2 x$

$x = \frac{- 48}{- 4}$

$y = 26 - 2 x$

$x = \frac{- 48}{- 4}$

$y = 26 - 2 x$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide

$- 48$ by

$- 4$ .

$x = 12$

$y = 26 - 2 x$

$x = 12$

$y = 26 - 2 x$

$x = 12$

$y = 26 - 2 x$

$x = 12$

$y = 26 - 2 x$

Step 4

Replace all occurrences of

$x$ with

$12$ in each equation.

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Step 4.1

Replace all occurrences of

$x$ in

$y = 26 - 2 x$ with

$12$ .

$y = 26 - 2 \cdot 12$

$x = 12$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify

$26 - 2 \cdot 12$ .

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Step 4.2.1.1

Multiply

$- 2$ by

$12$ .

$y = 26 - 24$

$x = 12$

Step 4.2.1.2

Subtract

$24$ from

$26$ .

$y = 2$

$x = 12$

$y = 2$

$x = 12$

$y = 2$

$x = 12$

$y = 2$

$x = 12$

Step 5

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

$(12, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(12, 2)$

Equation Form:

$x = 12, y = 2$

Step 7

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