Algebra Examples

$\frac{1}{2} x + y = - 1$ $y = \frac{1}{4} x - 4$

Step 1

Combine $\frac{1}{4}$ and $x$ .

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

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

Step 2

Replace all occurrences of $y$ with $\frac{x}{4} - 4$ in each equation.

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Step 2.1

Replace all occurrences of $y$ in $\frac{1}{2} x + y = - 1$ with $\frac{x}{4} - 4$ .

$\frac{1}{2} x + \frac{x}{4} - 4 = - 1$

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $\frac{1}{2} x + \frac{x}{4} - 4$ .

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Step 2.2.1.1

Remove parentheses.

$\frac{1}{2} x + \frac{x}{4} - 4 = - 1$

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

Step 2.2.1.2

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

$\frac{x}{2} + \frac{x}{4} - 4 = - 1$

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

Step 2.2.1.3

To write $\frac{x}{2}$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{x}{2} \cdot \frac{2}{2} + \frac{x}{4} - 4 = - 1$

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

Step 2.2.1.4

Write each expression with a common denominator of $4$ , by multiplying each by an appropriate factor of $1$ .

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Step 2.2.1.4.1

Multiply $\frac{x}{2}$ by $\frac{2}{2}$ .

$\frac{x \cdot 2}{2 \cdot 2} + \frac{x}{4} - 4 = - 1$

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

Step 2.2.1.4.2

Multiply $2$ by $2$ .

$\frac{x \cdot 2}{4} + \frac{x}{4} - 4 = - 1$

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

$\frac{x \cdot 2}{4} + \frac{x}{4} - 4 = - 1$

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

Step 2.2.1.5

Combine the numerators over the common denominator.

$\frac{x \cdot 2 + x}{4} - 4 = - 1$

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

Step 2.2.1.6

Add $x \cdot 2$ and $x$ .

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Step 2.2.1.6.1

Reorder $x$ and $2$ .

$\frac{2 \cdot x + x}{4} - 4 = - 1$

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

Step 2.2.1.6.2

Add $2 \cdot x$ and $x$ .

$\frac{3 \cdot x}{4} - 4 = - 1$

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

$\frac{3 x}{4} - 4 = - 1$

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

$\frac{3 x}{4} - 4 = - 1$

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

$\frac{3 x}{4} - 4 = - 1$

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

$\frac{3 x}{4} - 4 = - 1$

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

Step 3

Solve for $x$ in $\frac{3 x}{4} - 4 = - 1$ .

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Step 3.1

Move all terms not containing $x$ to the right side of the equation.

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Step 3.1.1

Add $4$ to both sides of the equation.

$\frac{3 x}{4} = - 1 + 4$

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

Step 3.1.2

Add $- 1$ and $4$ .

$\frac{3 x}{4} = 3$

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

$\frac{3 x}{4} = 3$

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

Step 3.2

Multiply both sides of the equation by $\frac{4}{3}$ .

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} \cdot 3$

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

Step 3.3

Simplify both sides of the equation.

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Step 3.3.1

Simplify the left side.

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Step 3.3.1.1

Simplify $\frac{4}{3} \cdot \frac{3 x}{4}$ .

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Step 3.3.1.1.1

Cancel the common factor of $4$ .

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Step 3.3.1.1.1.1

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 x}{4} = \frac{4}{3} \cdot 3$

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

Step 3.3.1.1.1.2

Rewrite the expression.

$\frac{1}{3} \cdot (3 x) = \frac{4}{3} \cdot 3$

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

$\frac{1}{3} \cdot (3 x) = \frac{4}{3} \cdot 3$

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

Step 3.3.1.1.2

Cancel the common factor of $3$ .

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Step 3.3.1.1.2.1

Factor $3$ out of $3 x$ .

$\frac{1}{3} \cdot (3 (x)) = \frac{4}{3} \cdot 3$

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

Step 3.3.1.1.2.2

Cancel the common factor.

$\frac{1}{3} \cdot (3 x) = \frac{4}{3} \cdot 3$

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

Step 3.3.1.1.2.3

Rewrite the expression.

$x = \frac{4}{3} \cdot 3$

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

$x = \frac{4}{3} \cdot 3$

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

$x = \frac{4}{3} \cdot 3$

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

$x = \frac{4}{3} \cdot 3$

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

Step 3.3.2

Simplify the right side.

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Step 3.3.2.1

Cancel the common factor of $3$ .

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Step 3.3.2.1.1

Cancel the common factor.

$x = \frac{4}{3} \cdot 3$

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

Step 3.3.2.1.2

Rewrite the expression.

$x = 4$

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

$x = 4$

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

$x = 4$

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

$x = 4$

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

$x = 4$

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

Step 4

Replace all occurrences of $x$ with $4$ in each equation.

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Step 4.1

Replace all occurrences of $x$ in $y = \frac{x}{4} - 4$ with $4$ .

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

$x = 4$

Step 4.2

Simplify the right side.

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Step 4.2.1

Simplify $\frac{4}{4} - 4$ .

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Step 4.2.1.1

Divide $4$ by $4$ .

$y = 1 - 4$

$x = 4$

Step 4.2.1.2

Subtract $4$ from $1$ .

$y = - 3$

$x = 4$

$y = - 3$

$x = 4$

$y = - 3$

$x = 4$

$y = - 3$

$x = 4$

Step 5

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

$(4, - 3)$

Step 6

The result can be shown in multiple forms.

Point Form:

$(4, - 3)$

Equation Form:

$x = 4, y = - 3$

Step 7