Precalculus Examples

3 x - y = 7

$3 x - y = 7$ ,

- 3 x + y = 5

$- 3 x + y = 5$

Step 1

Add

3 x

$3 x$ to both sides of the equation.

y = 5 + 3 x

$y = 5 + 3 x$

3 x - y = 7

$3 x - y = 7$

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

3 x - y = 7

$3 x - y = 7$ with

5 + 3 x

$5 + 3 x$ .

3 x - (5 + 3 x) = 7

$3 x - (5 + 3 x) = 7$

y = 5 + 3 x

$y = 5 + 3 x$

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify

3 x - (5 + 3 x)

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

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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.

3 x - 1 \cdot 5 - (3 x) = 7

$3 x - 1 \cdot 5 - (3 x) = 7$

y = 5 + 3 x

$y = 5 + 3 x$

Step 2.2.1.1.2

Multiply

- 1

$- 1$ by

5

$5$ .

3 x - 5 - (3 x) = 7

$3 x - 5 - (3 x) = 7$

y = 5 + 3 x

$y = 5 + 3 x$

Step 2.2.1.1.3

Multiply

3

$3$ by

- 1

$- 1$ .

3 x - 5 - 3 x = 7

$3 x - 5 - 3 x = 7$

y = 5 + 3 x

$y = 5 + 3 x$

3 x - 5 - 3 x = 7

$3 x - 5 - 3 x = 7$

y = 5 + 3 x

$y = 5 + 3 x$

Step 2.2.1.2

Combine the opposite terms in

3 x - 5 - 3 x

$3 x - 5 - 3 x$ .

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Step 2.2.1.2.1

Subtract

3 x

$3 x$ from

3 x

$3 x$ .

0 - 5 = 7

$0 - 5 = 7$

y = 5 + 3 x

$y = 5 + 3 x$

Step 2.2.1.2.2

Subtract

5

$5$ from

0

$0$ .

- 5 = 7

$- 5 = 7$

y = 5 + 3 x

$y = 5 + 3 x$

- 5 = 7

$- 5 = 7$

y = 5 + 3 x

$y = 5 + 3 x$

- 5 = 7

$- 5 = 7$

y = 5 + 3 x

$y = 5 + 3 x$

- 5 = 7

$- 5 = 7$

y = 5 + 3 x

$y = 5 + 3 x$

- 5 = 7

$- 5 = 7$

y = 5 + 3 x

$y = 5 + 3 x$

Step 3

Since

- 5 = 7

$- 5 = 7$ is not true, there is no solution.

No solution

Step 4

3 x - y = 7, - 3 x + y = 5

$3 x - y = 7, - 3 x + y = 5$

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

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