Finite Math Examples

3 x + y = 5

$3 x + y = 5$ ,

- 9 x - 3 y = 23

$- 9 x - 3 y = 23$

Step 1

Subtract

3 x

$3 x$ from both sides of the equation.

y = 5 - 3 x

$y = 5 - 3 x$

- 9 x - 3 y = 23

$- 9 x - 3 y = 23$

Step 2

Replace all occurrences of

y

$y$ with

5 - 3 x

$5 - 3 x$ in each equation.

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Step 2.1

Replace all occurrences of

y

$y$ in

- 9 x - 3 y = 23

$- 9 x - 3 y = 23$ with

5 - 3 x

$5 - 3 x$ .

- 9 x - 3 (5 - 3 x) = 23

$- 9 x - 3 (5 - 3 x) = 23$

y = 5 - 3 x

$y = 5 - 3 x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify

- 9 x - 3 (5 - 3 x)

$- 9 x - 3 (5 - 3 x)$ .

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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.

- 9 x - 3 \cdot 5 - 3 (- 3 x) = 23

$- 9 x - 3 \cdot 5 - 3 (- 3 x) = 23$

y = 5 - 3 x

$y = 5 - 3 x$

Step 2.2.1.1.2

Multiply

- 3

$- 3$ by

5

$5$ .

- 9 x - 15 - 3 (- 3 x) = 23

$- 9 x - 15 - 3 (- 3 x) = 23$

y = 5 - 3 x

$y = 5 - 3 x$

Step 2.2.1.1.3

Multiply

- 3

$- 3$ by

- 3

$- 3$ .

- 9 x - 15 + 9 x = 23

$- 9 x - 15 + 9 x = 23$

y = 5 - 3 x

$y = 5 - 3 x$

- 9 x - 15 + 9 x = 23

$- 9 x - 15 + 9 x = 23$

y = 5 - 3 x

$y = 5 - 3 x$

Step 2.2.1.2

Combine the opposite terms in

- 9 x - 15 + 9 x

$- 9 x - 15 + 9 x$ .

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Step 2.2.1.2.1

Add

- 9 x

$- 9 x$ and

9 x

$9 x$ .

0 - 15 = 23

$0 - 15 = 23$

y = 5 - 3 x

$y = 5 - 3 x$

Step 2.2.1.2.2

Subtract

15

$15$ from

0

$0$ .

- 15 = 23

$- 15 = 23$

y = 5 - 3 x

$y = 5 - 3 x$

- 15 = 23

$- 15 = 23$

y = 5 - 3 x

$y = 5 - 3 x$

- 15 = 23

$- 15 = 23$

y = 5 - 3 x

$y = 5 - 3 x$

- 15 = 23

$- 15 = 23$

y = 5 - 3 x

$y = 5 - 3 x$

- 15 = 23

$- 15 = 23$

y = 5 - 3 x

$y = 5 - 3 x$

Step 3

Since

- 15 = 23

$- 15 = 23$ is not true, there is no solution.

No solution

Step 4

⎡ ⎢ ⎣ \begin{matrix} x^{2} & \frac{1}{2} \sqrt{π} & \int x d x \end{matrix} ⎤ ⎥ ⎦

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