Algebra Examples

$2 x - y = 0$ $4 x - y = 0$

Step 1

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

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Step 1.1

Add $y$ to both sides of the equation.

$2 x = y$

$4 x - y = 0$

Step 1.2

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

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Step 1.2.1

Divide each term in $2 x = y$ by $2$ .

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

$4 x - y = 0$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Cancel the common factor of $2$ .

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Step 1.2.2.1.1

Cancel the common factor.

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

$4 x - y = 0$

Step 1.2.2.1.2

Divide $x$ by $1$ .

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

$4 x - y = 0$

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

$4 x - y = 0$

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

$4 x - y = 0$

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

$4 x - y = 0$

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

$4 x - y = 0$

Step 2

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

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Step 2.1

Replace all occurrences of $x$ in $4 x - y = 0$ with $\frac{y}{2}$ .

$4 (\frac{y}{2}) - y = 0$

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

Step 2.2

Simplify the left side.

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Step 2.2.1

Simplify $4 (\frac{y}{2}) - y$ .

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Step 2.2.1.1

Cancel the common factor of $2$ .

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Step 2.2.1.1.1

Factor $2$ out of $4$ .

$2 (2) (\frac{y}{2}) - y = 0$

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

Step 2.2.1.1.2

Cancel the common factor.

$2 \cdot (2 (\frac{y}{2})) - y = 0$

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

Step 2.2.1.1.3

Rewrite the expression.

$2 y - y = 0$

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

$2 y - y = 0$

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

Step 2.2.1.2

Subtract $y$ from $2 y$ .

$y = 0$

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

$y = 0$

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

$y = 0$

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

$y = 0$

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

Step 3

Replace all occurrences of $y$ with $0$ in each equation.

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Step 3.1

Replace all occurrences of $y$ in $x = \frac{y}{2}$ with $0$ .

$x = \frac{0}{2}$

$y = 0$

Step 3.2

Simplify the right side.

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Step 3.2.1

Divide $0$ by $2$ .

$x = 0$

$y = 0$

$x = 0$

$y = 0$

$x = 0$

$y = 0$

Step 4

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

$(0, 0)$

Step 5

The result can be shown in multiple forms.

Point Form:

$(0, 0)$

Equation Form:

$x = 0, y = 0$

Step 6