Algebra Examples

x + y = 8

$x + y = 8$ ,

x - y = 4

$x - y = 4$

Step 1

Subtract

y

$y$ from both sides of the equation.

x = 8 - y

$x = 8 - y$

x - y = 4

$x - y = 4$

Step 2

Replace all occurrences of

x

$x$ with

8 - y

$8 - y$ in each equation.

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Step 2.1

Replace all occurrences of

x

$x$ in

x - y = 4

$x - y = 4$ with

8 - y

$8 - y$ .

(8 - y) - y = 4

$(8 - y) - y = 4$

x = 8 - y

$x = 8 - y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Subtract

y

$y$ from

- y

$- y$ .

8 - 2 y = 4

$8 - 2 y = 4$

x = 8 - y

$x = 8 - y$

8 - 2 y = 4

$8 - 2 y = 4$

x = 8 - y

$x = 8 - y$

8 - 2 y = 4

$8 - 2 y = 4$

x = 8 - y

$x = 8 - y$

Step 3

Solve for

y

$y$ in

8 - 2 y = 4

$8 - 2 y = 4$ .

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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

8

$8$ from both sides of the equation.

- 2 y = 4 - 8

$- 2 y = 4 - 8$

x = 8 - y

$x = 8 - y$

Step 3.1.2

Subtract

8

$8$ from

4

$4$ .

- 2 y = - 4

$- 2 y = - 4$

x = 8 - y

$x = 8 - y$

- 2 y = - 4

$- 2 y = - 4$

x = 8 - y

$x = 8 - y$

Step 3.2

Divide each term in

- 2 y = - 4

$- 2 y = - 4$ by

- 2

$- 2$ and simplify.

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Step 3.2.1

Divide each term in

- 2 y = - 4

$- 2 y = - 4$ by

- 2

$- 2$ .

\frac{- 2 y}{- 2} = \frac{- 4}{- 2}

$\frac{- 2 y}{- 2} = \frac{- 4}{- 2}$

x = 8 - y

$x = 8 - y$

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{- 4}{- 2}

$\frac{- 2 y}{- 2} = \frac{- 4}{- 2}$

x = 8 - y

$x = 8 - y$

Step 3.2.2.1.2

Divide

y

$y$ by

1

$1$ .

y = \frac{- 4}{- 2}

$y = \frac{- 4}{- 2}$

x = 8 - y

$x = 8 - y$

y = \frac{- 4}{- 2}

$y = \frac{- 4}{- 2}$

x = 8 - y

$x = 8 - y$

y = \frac{- 4}{- 2}

$y = \frac{- 4}{- 2}$

x = 8 - y

$x = 8 - y$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Divide

- 4

$- 4$ by

- 2

$- 2$ .

y = 2

$y = 2$

x = 8 - y

$x = 8 - y$

y = 2

$y = 2$

x = 8 - y

$x = 8 - y$

y = 2

$y = 2$

x = 8 - y

$x = 8 - y$

y = 2

$y = 2$

x = 8 - y

$x = 8 - y$

Step 4

Replace all occurrences of

y

$y$ with

2

$2$ in each equation.

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Step 4.1

Replace all occurrences of

y

$y$ in

x = 8 - y

$x = 8 - y$ with

2

$2$ .

x = 8 - (2)

$x = 8 - (2)$

y = 2

$y = 2$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify

8 - (2)

$8 - (2)$ .

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Step 4.2.1.1

Multiply

- 1

$- 1$ by

2

$2$ .

x = 8 - 2

$x = 8 - 2$

y = 2

$y = 2$

Step 4.2.1.2

Subtract

2

$2$ from

8

$8$ .

x = 6

$x = 6$

y = 2

$y = 2$

x = 6

$x = 6$

y = 2

$y = 2$

x = 6

$x = 6$

y = 2

$y = 2$

x = 6

$x = 6$

y = 2

$y = 2$

Step 5

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

(6, 2)

$(6, 2)$

Step 6

The result can be shown in multiple forms.

Point Form:

(6, 2)

$(6, 2)$

Equation Form:

x = 6, y = 2

$x = 6, y = 2$

Step 7

x + y = 8, x - y = 4

$x + y = 8, x - y = 4$

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

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