Pre-Algebra Examples

$x + 2 y = 2$ , $x - 2 y = 0$

Step 1

Subtract $2 y$ from both sides of the equation.

$x = 2 - 2 y$

$x - 2 y = 0$

Step 2

Replace all occurrences of $x$ with $2 - 2 y$ in each equation.

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Step 2.1

Replace all occurrences of $x$ in $x - 2 y = 0$ with $2 - 2 y$ .

$(2 - 2 y) - 2 y = 0$

$x = 2 - 2 y$

Step 2.2

Simplify the left side.

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Step 2.2.1

Subtract $2 y$ from $- 2 y$ .

$2 - 4 y = 0$

$x = 2 - 2 y$

$2 - 4 y = 0$

$x = 2 - 2 y$

$2 - 4 y = 0$

$x = 2 - 2 y$

Step 3

Solve for $y$ in $2 - 4 y = 0$ .

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Step 3.1

Subtract $2$ from both sides of the equation.

$- 4 y = - 2$

$x = 2 - 2 y$

Step 3.2

Divide each term in $- 4 y = - 2$ by $- 4$ and simplify.

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Step 3.2.1

Divide each term in $- 4 y = - 2$ by $- 4$ .

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

$x = 2 - 2 y$

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.

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

$x = 2 - 2 y$

Step 3.2.2.1.2

Divide $y$ by $1$ .

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

$x = 2 - 2 y$

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

$x = 2 - 2 y$

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

$x = 2 - 2 y$

Step 3.2.3

Simplify the right side.

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Step 3.2.3.1

Cancel the common factor of $- 2$ and $- 4$ .

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Step 3.2.3.1.1

Factor $- 2$ out of $- 2$ .

$y = \frac{- 2 \cdot 1}{- 4}$

$x = 2 - 2 y$

Step 3.2.3.1.2

Cancel the common factors.

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Step 3.2.3.1.2.1

Factor $- 2$ out of $- 4$ .

$y = \frac{- 2 \cdot 1}{- 2 \cdot 2}$

$x = 2 - 2 y$

Step 3.2.3.1.2.2

Cancel the common factor.

$y = \frac{- 2 \cdot 1}{- 2 \cdot 2}$

$x = 2 - 2 y$

Step 3.2.3.1.2.3

Rewrite the expression.

$y = \frac{1}{2}$

$x = 2 - 2 y$

$y = \frac{1}{2}$

$x = 2 - 2 y$

$y = \frac{1}{2}$

$x = 2 - 2 y$

$y = \frac{1}{2}$

$x = 2 - 2 y$

$y = \frac{1}{2}$

$x = 2 - 2 y$

$y = \frac{1}{2}$

$x = 2 - 2 y$

Step 4

Replace all occurrences of $y$ with $\frac{1}{2}$ in each equation.

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Step 4.1

Replace all occurrences of $y$ in $x = 2 - 2 y$ with $\frac{1}{2}$ .

$x = 2 - 2 (\frac{1}{2})$

$y = \frac{1}{2}$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $2 - 2 (\frac{1}{2})$ .

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Step 4.2.1.1

Cancel the common factor of $2$ .

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Step 4.2.1.1.1

Factor $2$ out of $- 2$ .

$x = 2 + 2 (- 1) (\frac{1}{2})$

$y = \frac{1}{2}$

Step 4.2.1.1.2

Cancel the common factor.

$x = 2 + 2 \cdot (- 1 (\frac{1}{2}))$

$y = \frac{1}{2}$

Step 4.2.1.1.3

Rewrite the expression.

$x = 2 - 1$

$y = \frac{1}{2}$

$x = 2 - 1$

$y = \frac{1}{2}$

Step 4.2.1.2

Subtract $1$ from $2$ .

$x = 1$

$y = \frac{1}{2}$

$x = 1$

$y = \frac{1}{2}$

$x = 1$

$y = \frac{1}{2}$

$x = 1$

$y = \frac{1}{2}$

Step 5

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

$(1, \frac{1}{2})$

Step 6

The result can be shown in multiple forms.

Point Form:

$(1, \frac{1}{2})$

Equation Form:

$x = 1, y = \frac{1}{2}$

Step 7