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Precalculus Examples

x + y = 4

$x + y = 4$ ,

x - y = 2

$x - y = 2$

Step 1

Subtract

y

$y$ from both sides of the equation.

x = 4 - y

$x = 4 - y$

x - y = 2

$x - y = 2$

Step 2

Replace all occurrences of

x

$x$ with

4 - y

$4 - y$ in each equation.

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Step 2.1

Replace all occurrences of

x

$x$ in

x - y = 2

$x - y = 2$ with

4 - y

$4 - y$ .

(4 - y) - y = 2

$(4 - y) - y = 2$

x = 4 - y

$x = 4 - y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Subtract

y

$y$ from

- y

$- y$ .

4 - 2 y = 2

$4 - 2 y = 2$

x = 4 - y

$x = 4 - y$

4 - 2 y = 2

$4 - 2 y = 2$

x = 4 - y

$x = 4 - y$

4 - 2 y = 2

$4 - 2 y = 2$

x = 4 - y

$x = 4 - y$

Step 3

Solve for

y

$y$ in

4 - 2 y = 2

$4 - 2 y = 2$ .

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Step 3.1

Move all terms not containing

y

$y$ to the right side of the equation.

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Step 3.1.1

Subtract

4

$4$ from both sides of the equation.

- 2 y = 2 - 4

$- 2 y = 2 - 4$

x = 4 - y

$x = 4 - y$

Step 3.1.2

Subtract

4

$4$ from

2

$2$ .

- 2 y = - 2

$- 2 y = - 2$

x = 4 - y

$x = 4 - y$

- 2 y = - 2

$- 2 y = - 2$

x = 4 - y

$x = 4 - y$

Step 3.2

Divide each term in

- 2 y = - 2

$- 2 y = - 2$ by

- 2

$- 2$ and simplify.

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Step 3.2.1

Divide each term in

- 2 y = - 2

$- 2 y = - 2$ by

- 2

$- 2$ .

\frac{- 2 y}{- 2} = \frac{- 2}{- 2}

$\frac{- 2 y}{- 2} = \frac{- 2}{- 2}$

x = 4 - y

$x = 4 - y$

Step 3.2.2

Simplify the left side.

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Step 3.2.2.1

Cancel the common factor of

- 2

$- 2$ .

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Step 3.2.2.1.1

Cancel the common factor.

$\frac{- 2 y}{- 2} = \frac{- 2}{- 2}$

$x = 4 - y$

Step 3.2.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{- 2}{- 2}$

$x = 4 - y$

$y = \frac{- 2}{- 2}$

$x = 4 - y$

$y = \frac{- 2}{- 2}$

$x = 4 - y$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide

$- 2$ by

$- 2$ .

$y = 1$

$x = 4 - y$

$y = 1$

$x = 4 - y$

$y = 1$

$x = 4 - y$

$y = 1$

$x = 4 - y$

Step 4

Replace all occurrences of

$y$ with

$1$ in each equation.

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Step 4.1

Replace all occurrences of

$y$ in

$x = 4 - y$ with

$1$ .

$x = 4 - (1)$

$y = 1$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify

$4 - (1)$ .

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Step 4.2.1.1

Multiply

$- 1$ by

$1$ .

$x = 4 - 1$

$y = 1$

Step 4.2.1.2

Subtract

$1$ from

$4$ .

$x = 3$

$y = 1$

$x = 3$

$y = 1$

$x = 3$

$y = 1$

$x = 3$

$y = 1$

Step 5

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

$(3, 1)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(3, 1)$

Equation Form:

$x = 3, y = 1$

Step 7

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