Algebra Examples

$- 3 x + 5 y = 2 x + 3 y$

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

Subtract $3 y$ from both sides of the equation.

$- 3 x + 5 y - 3 y = 2 x$

Step 1.1.2

Subtract $3 y$ from $5 y$ .

$- 3 x + 2 y = 2 x$

Step 1.2

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

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Step 1.2.1

Add $3 x$ to both sides of the equation.

$2 y = 2 x + 3 x$

Step 1.2.2

Add $2 x$ and $3 x$ .

$2 y = 5 x$

Step 1.3

Divide each term in $2 y = 5 x$ by $2$ and simplify.

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Step 1.3.1

Divide each term in $2 y = 5 x$ by $2$ .

$\frac{2 y}{2} = \frac{5 x}{2}$

Step 1.3.2

Simplify the left side.

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Step 1.3.2.1

Cancel the common factor of $2$ .

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Step 1.3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{5 x}{2}$

Step 1.3.2.1.2

Divide $y$ by $1$ .

$y = \frac{5 x}{2}$

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.

$y = \frac{5 (0)}{2}$

Step 3.2

Simplify $\frac{5 (0)}{2}$ .

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Step 3.2.1

Cancel the common factor of $0$ and $2$ .

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Step 3.2.1.1

Factor $2$ out of $5 (0)$ .

$y = \frac{2 (5 \cdot (0))}{2}$

Step 3.2.1.2

Cancel the common factors.

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Step 3.2.1.2.1

Factor $2$ out of $2$ .

$y = \frac{2 (5 \cdot (0))}{2 (1)}$

Step 3.2.1.2.2

Cancel the common factor.

$y = \frac{2 (5 \cdot (0))}{2 \cdot 1}$

Step 3.2.1.2.3

Rewrite the expression.

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

Step 3.2.1.2.4

Divide $5 \cdot (0)$ by $1$ .

$y = 5 \cdot (0)$

Step 3.2.2

Multiply $5$ 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.

$y = \frac{5 (1)}{2}$

Step 4.2

Multiply $5$ by $1$ .

$y = \frac{5}{2}$

Step 4.3

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

$(1, \frac{5}{2})$

Step 5

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

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Step 5.1

Remove parentheses.

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

Step 5.2

Cancel the common factor of $2$ .

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Step 5.2.1

Cancel the common factor.

$y = \frac{5 \cdot 2}{2}$

Step 5.2.2

Divide $5$ by $1$ .

$y = 5$

Step 5.3

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

$(2, 5)$

Step 6

These are three possible solutions to the equation.

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

Step 7