Algebra Examples

$- 2 x + 4 y = 9$ , $8 y = 4 x + 18$

Step 1

Add $2 x$ to both sides of the equation.

$4 y = 9 + 2 x$

$8 y = 4 x + 18$

Step 2

Divide each term in $4 y = 9 + 2 x$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 y = 9 + 2 x$ by $4$ .

$\frac{4 y}{4} = \frac{9}{4} + \frac{2 x}{4}$

$8 y = 4 x + 18$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 y}{4} = \frac{9}{4} + \frac{2 x}{4}$

$8 y = 4 x + 18$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{9}{4} + \frac{2 x}{4}$

$8 y = 4 x + 18$

$y = \frac{9}{4} + \frac{2 x}{4}$

$8 y = 4 x + 18$

$y = \frac{9}{4} + \frac{2 x}{4}$

$8 y = 4 x + 18$

Step 2.3

Simplify the right side.

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Step 2.3.1

Cancel the common factor of $2$ and $4$ .

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Step 2.3.1.1

Factor $2$ out of $2 x$ .

$y = \frac{9}{4} + \frac{2 (x)}{4}$

$8 y = 4 x + 18$

Step 2.3.1.2

Cancel the common factors.

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Step 2.3.1.2.1

Factor $2$ out of $4$ .

$y = \frac{9}{4} + \frac{2 x}{2 \cdot 2}$

$8 y = 4 x + 18$

Step 2.3.1.2.2

Cancel the common factor.

$y = \frac{9}{4} + \frac{2 x}{2 \cdot 2}$

$8 y = 4 x + 18$

Step 2.3.1.2.3

Rewrite the expression.

$y = \frac{9}{4} + \frac{x}{2}$

$8 y = 4 x + 18$

$y = \frac{9}{4} + \frac{x}{2}$

$8 y = 4 x + 18$

$y = \frac{9}{4} + \frac{x}{2}$

$8 y = 4 x + 18$

$y = \frac{9}{4} + \frac{x}{2}$

$8 y = 4 x + 18$

$y = \frac{9}{4} + \frac{x}{2}$

$8 y = 4 x + 18$

Step 3

Divide each term in $8 y = 4 x + 18$ by $8$ and simplify.

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Step 3.1

Divide each term in $8 y = 4 x + 18$ by $8$ .

$\frac{8 y}{8} = \frac{4 x}{8} + \frac{18}{8}$

$y = \frac{9}{4} + \frac{x}{2}$

Step 3.2

Simplify the left side.

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Step 3.2.1

Cancel the common factor of $8$ .

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Step 3.2.1.1

Cancel the common factor.

$\frac{8 y}{8} = \frac{4 x}{8} + \frac{18}{8}$

$y = \frac{9}{4} + \frac{x}{2}$

Step 3.2.1.2

Divide $y$ by $1$ .

$y = \frac{4 x}{8} + \frac{18}{8}$

$y = \frac{9}{4} + \frac{x}{2}$

$y = \frac{4 x}{8} + \frac{18}{8}$

$y = \frac{9}{4} + \frac{x}{2}$

$y = \frac{4 x}{8} + \frac{18}{8}$

$y = \frac{9}{4} + \frac{x}{2}$

Step 3.3

Simplify the right side.

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Step 3.3.1

Simplify each term.

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Step 3.3.1.1

Cancel the common factor of $4$ and $8$ .

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Step 3.3.1.1.1

Factor $4$ out of $4 x$ .

$y = \frac{4 (x)}{8} + \frac{18}{8}$

$y = \frac{9}{4} + \frac{x}{2}$

Step 3.3.1.1.2

Cancel the common factors.

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Step 3.3.1.1.2.1

Factor $4$ out of $8$ .

$y = \frac{4 x}{4 \cdot 2} + \frac{18}{8}$

$y = \frac{9}{4} + \frac{x}{2}$

Step 3.3.1.1.2.2

Cancel the common factor.

$y = \frac{4 x}{4 \cdot 2} + \frac{18}{8}$

$y = \frac{9}{4} + \frac{x}{2}$

Step 3.3.1.1.2.3

Rewrite the expression.

$y = \frac{x}{2} + \frac{18}{8}$

$y = \frac{9}{4} + \frac{x}{2}$

$y = \frac{x}{2} + \frac{18}{8}$

$y = \frac{9}{4} + \frac{x}{2}$

$y = \frac{x}{2} + \frac{18}{8}$

$y = \frac{9}{4} + \frac{x}{2}$

Step 3.3.1.2

Cancel the common factor of $18$ and $8$ .

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Step 3.3.1.2.1

Factor $2$ out of $18$ .

$y = \frac{x}{2} + \frac{2 (9)}{8}$

$y = \frac{9}{4} + \frac{x}{2}$

Step 3.3.1.2.2

Cancel the common factors.

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Step 3.3.1.2.2.1

Factor $2$ out of $8$ .

$y = \frac{x}{2} + \frac{2 \cdot 9}{2 \cdot 4}$

$y = \frac{9}{4} + \frac{x}{2}$

Step 3.3.1.2.2.2

Cancel the common factor.

$y = \frac{x}{2} + \frac{2 \cdot 9}{2 \cdot 4}$

$y = \frac{9}{4} + \frac{x}{2}$

Step 3.3.1.2.2.3

Rewrite the expression.

$y = \frac{x}{2} + \frac{9}{4}$

$y = \frac{9}{4} + \frac{x}{2}$

$y = \frac{x}{2} + \frac{9}{4}$

$y = \frac{9}{4} + \frac{x}{2}$

$y = \frac{x}{2} + \frac{9}{4}$

$y = \frac{9}{4} + \frac{x}{2}$

$y = \frac{x}{2} + \frac{9}{4}$

$y = \frac{9}{4} + \frac{x}{2}$

$y = \frac{x}{2} + \frac{9}{4}$

$y = \frac{9}{4} + \frac{x}{2}$

$y = \frac{x}{2} + \frac{9}{4}$

$y = \frac{9}{4} + \frac{x}{2}$

Step 4

Create a graph to locate the intersection of the equations. The intersection of the system of equations is the solution.

Always true

Step 5