Algebra Examples

3 x + 2 y = 6

$3 x + 2 y = 6$

Step 1

Substitute

- 2

$- 2$ for

x

$x$ and find the result for

y

$y$ .

3 (- 2) + 2 y = 6

$3 (- 2) + 2 y = 6$

Step 2

Solve the equation for

y

$y$ .

Tap for more steps...

Step 2.1

Multiply

3

$3$ by

- 2

$- 2$ .

- 6 + 2 y = 6

$- 6 + 2 y = 6$

Step 2.2

Move all terms not containing

y

$y$ to the right side of the equation.

Tap for more steps...

Step 2.2.1

Add

6

$6$ to both sides of the equation.

2 y = 6 + 6

$2 y = 6 + 6$

Step 2.2.2

Add

6

$6$ and

6

$6$ .

2 y = 12

$2 y = 12$

2 y = 12

$2 y = 12$

Step 2.3

Divide each term in

2 y = 12

$2 y = 12$ by

2

$2$ and simplify.

Tap for more steps...

Step 2.3.1

Divide each term in

2 y = 12

$2 y = 12$ by

2

$2$ .

\frac{2 y}{2} = \frac{12}{2}

$\frac{2 y}{2} = \frac{12}{2}$

Step 2.3.2

Simplify the left side.

Tap for more steps...

Step 2.3.2.1

Cancel the common factor of

2

$2$ .

Tap for more steps...

Step 2.3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{12}{2}$

Step 2.3.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{12}{2}$

Step 2.3.3

Simplify the right side.

Tap for more steps...

Step 2.3.3.1

Divide

$12$ by

$2$ .

$y = 6$

Step 3

Substitute

$- 1$ for

$x$ and find the result for

$y$ .

$3 (- 1) + 2 y = 6$

Step 4

Solve the equation for

$y$ .

Tap for more steps...

Step 4.1

Multiply

$3$ by

$- 1$ .

$- 3 + 2 y = 6$

Step 4.2

Move all terms not containing

$y$ to the right side of the equation.

Tap for more steps...

Step 4.2.1

Add

$3$ to both sides of the equation.

$2 y = 6 + 3$

Step 4.2.2

Add

$6$ and

$3$ .

$2 y = 9$

Step 4.3

Divide each term in

$2 y = 9$ by

$2$ and simplify.

Tap for more steps...

Step 4.3.1

Divide each term in

$2 y = 9$ by

$2$ .

$\frac{2 y}{2} = \frac{9}{2}$

Step 4.3.2

Simplify the left side.

Tap for more steps...

Step 4.3.2.1

Cancel the common factor of

$2$ .

Tap for more steps...

Step 4.3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{9}{2}$

Step 4.3.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{9}{2}$

Step 5

Substitute

$0$ for

$x$ and find the result for

$y$ .

$3 (0) + 2 y = 6$

Step 6

Solve the equation for

$y$ .

Tap for more steps...

Step 6.1

Simplify

$3 (0) + 2 y$ .

Tap for more steps...

Step 6.1.1

Multiply

$3$ by

$0$ .

$0 + 2 y = 6$

Step 6.1.2

Add

$0$ and

$2 y$ .

$2 y = 6$

Step 6.2

Divide each term in

$2 y = 6$ by

$2$ and simplify.

Tap for more steps...

Step 6.2.1

Divide each term in

$2 y = 6$ by

$2$ .

$\frac{2 y}{2} = \frac{6}{2}$

Step 6.2.2

Simplify the left side.

Tap for more steps...

Step 6.2.2.1

Cancel the common factor of

$2$ .

Tap for more steps...

Step 6.2.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{6}{2}$

Step 6.2.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{6}{2}$

Step 6.2.3

Simplify the right side.

Tap for more steps...

Step 6.2.3.1

Divide

$6$ by

$2$ .

$y = 3$

Step 7

Substitute

$1$ for

$x$ and find the result for

$y$ .

$3 (1) + 2 y = 6$

Step 8

Solve the equation for

$y$ .

Tap for more steps...

Step 8.1

Multiply

$3$ by

$1$ .

$3 + 2 y = 6$

Step 8.2

Move all terms not containing

$y$ to the right side of the equation.

Tap for more steps...

Step 8.2.1

Subtract

$3$ from both sides of the equation.

$2 y = 6 - 3$

Step 8.2.2

Subtract

$3$ from

$6$ .

$2 y = 3$

Step 8.3

Divide each term in

$2 y = 3$ by

$2$ and simplify.

Tap for more steps...

Step 8.3.1

Divide each term in

$2 y = 3$ by

$2$ .

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

Step 8.3.2

Simplify the left side.

Tap for more steps...

Step 8.3.2.1

Cancel the common factor of

$2$ .

Tap for more steps...

Step 8.3.2.1.1

Cancel the common factor.

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

Step 8.3.2.1.2

Divide

$y$ by

$1$ .

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

Step 9

Substitute

$2$ for

$x$ and find the result for

$y$ .

$3 (2) + 2 y = 6$

Step 10

Solve the equation for

$y$ .

Tap for more steps...

Step 10.1

Multiply

$3$ by

$2$ .

$6 + 2 y = 6$

Step 10.2

Move all terms not containing

$y$ to the right side of the equation.

Tap for more steps...

Step 10.2.1

Subtract

$6$ from both sides of the equation.

$2 y = 6 - 6$

Step 10.2.2

Subtract

$6$ from

$6$ .

$2 y = 0$

Step 10.3

Divide each term in

$2 y = 0$ by

$2$ and simplify.

Tap for more steps...

Step 10.3.1

Divide each term in

$2 y = 0$ by

$2$ .

$\frac{2 y}{2} = \frac{0}{2}$

Step 10.3.2

Simplify the left side.

Tap for more steps...

Step 10.3.2.1

Cancel the common factor of

$2$ .

Tap for more steps...

Step 10.3.2.1.1

Cancel the common factor.

$\frac{2 y}{2} = \frac{0}{2}$

Step 10.3.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{0}{2}$

Step 10.3.3

Simplify the right side.

Tap for more steps...

Step 10.3.3.1

Divide

$0$ by

$2$ .

$y = 0$

Step 11

This is a table of possible values to use when graphing the equation.

$\begin{array}{c} x & y \\ - 2 & 6 \\ - 1 & \frac{9}{2} \\ 0 & 3 \\ 1 & \frac{3}{2} \\ 2 & 0 \end{array}$

Step 12