Algebra Examples

$2 x + 4 y = 6 x - y$

Step 1

Solve the equation for $y$ .

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Step 1.1

Move all terms containing $y$ to the left side of the equation.

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Step 1.1.1

Add $y$ to both sides of the equation.

$2 x + 4 y + y = 6 x$

Step 1.1.2

Add $4 y$ and $y$ .

$2 x + 5 y = 6 x$

Step 1.2

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

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Step 1.2.1

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

$5 y = 6 x - 2 x$

Step 1.2.2

Subtract $2 x$ from $6 x$ .

$5 y = 4 x$

Step 1.3

Divide each term in $5 y = 4 x$ by $5$ and simplify.

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Step 1.3.1

Divide each term in $5 y = 4 x$ by $5$ .

$\frac{5 y}{5} = \frac{4 x}{5}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $5$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{5 y}{5} = \frac{4 x}{5}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{4 x}{5}$

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.

$y = \frac{4 (0)}{5}$

Step 3.2

Simplify $\frac{4 (0)}{5}$ .

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Step 3.2.1

Cancel the common factor of $0$ and $5$ .

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Step 3.2.1.1

Factor $5$ out of $4 (0)$ .

$y = \frac{5 (4 \cdot (0))}{5}$

Step 3.2.1.2

Cancel the common factors.

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Step 3.2.1.2.1

Factor $5$ out of $5$ .

$y = \frac{5 (4 \cdot (0))}{5 (1)}$

Step 3.2.1.2.2

Cancel the common factor.

$y = \frac{5 (4 \cdot (0))}{5 \cdot 1}$

Step 3.2.1.2.3

Rewrite the expression.

$y = \frac{4 \cdot (0)}{1}$

Step 3.2.1.2.4

Divide $4 \cdot (0)$ by $1$ .

$y = 4 \cdot (0)$

Step 3.2.2

Multiply $4$ by $0$ .

$y = 0$

Step 3.3

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

$(0, 0)$

Step 4

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

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Step 4.1

Remove parentheses.

$y = \frac{4 (1)}{5}$

Step 4.2

Multiply $4$ by $1$ .

$y = \frac{4}{5}$

Step 4.3

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

$(1, \frac{4}{5})$

Step 5

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

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Step 5.1

Remove parentheses.

$y = \frac{4 (2)}{5}$

Step 5.2

Multiply $4$ by $2$ .

$y = \frac{8}{5}$

Step 5.3

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

$(2, \frac{8}{5})$

Step 6

These are three possible solutions to the equation.

$(0, 0), (1, \frac{4}{5}), (2, \frac{8}{5})$

Step 7