Algebra Examples

$3 x + 2 y = 6$ $y = - \frac{5}{2} x + 1$

Step 1

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

$2 y = 6 - 3 x$

$y = - \frac{5}{2} x + 1$

Step 2

Divide each term in $2 y = 6 - 3 x$ by $2$ and simplify.

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Step 2.1

Divide each term in $2 y = 6 - 3 x$ by $2$ .

$\frac{2 y}{2} = \frac{6}{2} + \frac{- 3 x}{2}$

$y = - \frac{5}{2} x + 1$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $2$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{6}{2} + \frac{- 3 x}{2}$

$y = - \frac{5}{2} x + 1$

Step 2.2.1.2

Divide $y$ by $1$ .

$y = \frac{6}{2} + \frac{- 3 x}{2}$

$y = - \frac{5}{2} x + 1$

$y = \frac{6}{2} + \frac{- 3 x}{2}$

$y = - \frac{5}{2} x + 1$

$y = \frac{6}{2} + \frac{- 3 x}{2}$

$y = - \frac{5}{2} x + 1$

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 $6$ by $2$ .

$y = 3 + \frac{- 3 x}{2}$

$y = - \frac{5}{2} x + 1$

Step 2.3.1.2

Move the negative in front of the fraction.

$y = 3 - \frac{3 x}{2}$

$y = - \frac{5}{2} x + 1$

$y = 3 - \frac{3 x}{2}$

$y = - \frac{5}{2} x + 1$

$y = 3 - \frac{3 x}{2}$

$y = - \frac{5}{2} x + 1$

$y = 3 - \frac{3 x}{2}$

$y = - \frac{5}{2} x + 1$

Step 3

Simplify each term.

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Step 3.1

Combine $x$ and $\frac{5}{2}$ .

$y = - \frac{x \cdot 5}{2} + 1$

$y = 3 - \frac{3 x}{2}$

Step 3.2

Move $5$ to the left of $x$ .

$y = - \frac{5 x}{2} + 1$

$y = 3 - \frac{3 x}{2}$

$y = - \frac{5 x}{2} + 1$

$y = 3 - \frac{3 x}{2}$

Step 4

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

$(- 2, 6)$

Step 5