Algebra Examples

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

Step 1

Solve the equation for $y$ .

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Step 1.1

Combine $\frac{1}{2}$ and $y$ .

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

Step 1.2

Subtract $x$ from both sides of the equation.

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

Step 1.3

Multiply both sides of the equation by $2$ .

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

Step 1.4

Simplify both sides of the equation.

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Step 1.4.1

Simplify the left side.

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Step 1.4.1.1

Cancel the common factor of $2$ .

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Step 1.4.1.1.1

Cancel the common factor.

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

Step 1.4.1.1.2

Rewrite the expression.

$y = 2 (1 - x)$

Step 1.4.2

Simplify the right side.

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Step 1.4.2.1

Simplify $2 (1 - x)$ .

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Step 1.4.2.1.1

Apply the distributive property.

$y = 2 \cdot 1 + 2 (- x)$

Step 1.4.2.1.2

Multiply.

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Step 1.4.2.1.2.1

Multiply $2$ by $1$ .

$y = 2 + 2 (- x)$

Step 1.4.2.1.2.2

Multiply $- 1$ by $2$ .

$y = 2 - 2 x$

Step 1.5

Reorder $2$ and $- 2 x$ .

$y = - 2 x + 2$

Step 2

Choose any value for $x$ that is in the domain to plug into the equation.

Step 3

Choose $0$ to substitute in for $x$ to find the ordered pair.

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Step 3.1

Remove parentheses.

$y = - 2 \cdot 0 + 2$

Step 3.2

Simplify $- 2 \cdot 0 + 2$ .

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Step 3.2.1

Multiply $- 2$ by $0$ .

$y = 0 + 2$

Step 3.2.2

Add $0$ and $2$ .

$y = 2$

Step 3.3

Use the $x$ and $y$ values to form the ordered pair.

$(0, 2)$

Step 4

Choose $1$ to substitute in for $x$ to find the ordered pair.

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Step 4.1

Remove parentheses.

$y = - 2 \cdot 1 + 2$

Step 4.2

Simplify $- 2 \cdot 1 + 2$ .

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Step 4.2.1

Multiply $- 2$ by $1$ .

$y = - 2 + 2$

Step 4.2.2

Add $- 2$ and $2$ .

$y = 0$

Step 4.3

Use the $x$ and $y$ values to form the ordered pair.

$(1, 0)$

Step 5

Choose $2$ to substitute in for $x$ to find the ordered pair.

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Step 5.1

Remove parentheses.

$y = - 2 \cdot 2 + 2$

Step 5.2

Simplify $- 2 \cdot 2 + 2$ .

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Step 5.2.1

Multiply $- 2$ by $2$ .

$y = - 4 + 2$

Step 5.2.2

Add $- 4$ and $2$ .

$y = - 2$

Step 5.3

Use the $x$ and $y$ values to form the ordered pair.

$(2, - 2)$

Step 6

These are three possible solutions to the equation.

$(0, 2), (1, 0), (2, - 2)$

Step 7