Algebra Examples

$y = - 2 x + 3$ , $2 x + 4 y = 8$

Step 1

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

$4 y = 8 - 2 x$

$y = - 2 x + 3$

Step 2

Divide each term in $4 y = 8 - 2 x$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 y = 8 - 2 x$ by $4$ .

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

$y = - 2 x + 3$

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.

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

$y = - 2 x + 3$

Step 2.2.1.2

Divide $y$ by $1$ .

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

$y = - 2 x + 3$

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

$y = - 2 x + 3$

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

$y = - 2 x + 3$

Step 2.3

Simplify the right side.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Divide $8$ by $4$ .

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

$y = - 2 x + 3$

Step 2.3.1.2

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

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Step 2.3.1.2.1

Factor $2$ out of $- 2 x$ .

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

$y = - 2 x + 3$

Step 2.3.1.2.2

Cancel the common factors.

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Step 2.3.1.2.2.1

Factor $2$ out of $4$ .

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

$y = - 2 x + 3$

Step 2.3.1.2.2.2

Cancel the common factor.

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

$y = - 2 x + 3$

Step 2.3.1.2.2.3

Rewrite the expression.

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

$y = - 2 x + 3$

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

$y = - 2 x + 3$

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

$y = - 2 x + 3$

Step 2.3.1.3

Move the negative in front of the fraction.

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

$y = - 2 x + 3$

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

$y = - 2 x + 3$

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

$y = - 2 x + 3$

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

$y = - 2 x + 3$

Step 3

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

$(\frac{2}{3}, \frac{5}{3})$

Step 4