Algebra Examples

3 x - 4 y = 12

$3 x - 4 y = 12$

Step 1

Find the x-intercepts.

Tap for more steps...

Step 1.1

To find the x-intercept(s), substitute in

0

$0$ for

y

$y$ and solve for

x

$x$ .

3 x - 4 \cdot 0 = 12

$3 x - 4 \cdot 0 = 12$

Step 1.2

Solve the equation.

Tap for more steps...

Step 1.2.1

Simplify

3 x - 4 \cdot 0

$3 x - 4 \cdot 0$ .

Tap for more steps...

Step 1.2.1.1

Multiply

- 4

$- 4$ by

0

$0$ .

3 x + 0 = 12

$3 x + 0 = 12$

Step 1.2.1.2

Add

3 x

$3 x$ and

0

$0$ .

3 x = 12

$3 x = 12$

3 x = 12

$3 x = 12$

Step 1.2.2

Divide each term in

3 x = 12

$3 x = 12$ by

3

$3$ and simplify.

Tap for more steps...

Step 1.2.2.1

Divide each term in

3 x = 12

$3 x = 12$ by

3

$3$ .

\frac{3 x}{3} = \frac{12}{3}

$\frac{3 x}{3} = \frac{12}{3}$

Step 1.2.2.2

Simplify the left side.

Tap for more steps...

Step 1.2.2.2.1

Cancel the common factor of

3

$3$ .

Tap for more steps...

Step 1.2.2.2.1.1

Cancel the common factor.

\frac{3 x}{3} = \frac{12}{3}

$\frac{3 x}{3} = \frac{12}{3}$

Step 1.2.2.2.1.2

Divide

x

$x$ by

1

$1$ .

x = \frac{12}{3}

$x = \frac{12}{3}$

x = \frac{12}{3}

$x = \frac{12}{3}$

x = \frac{12}{3}

$x = \frac{12}{3}$

Step 1.2.2.3

Simplify the right side.

Tap for more steps...

Step 1.2.2.3.1

Divide

12

$12$ by

3

$3$ .

x = 4

$x = 4$

x = 4

$x = 4$

x = 4

$x = 4$

x = 4

$x = 4$

Step 1.3

x-intercept(s) in point form.

x-intercept(s):

(4, 0)

$(4, 0)$

x-intercept(s):

(4, 0)

$(4, 0)$

Step 2

Find the y-intercepts.

Tap for more steps...

Step 2.1

To find the y-intercept(s), substitute in

0

$0$ for

x

$x$ and solve for

y

$y$ .

3 (0) - 4 y = 12

$3 (0) - 4 y = 12$

Step 2.2

Solve the equation.

Tap for more steps...

Step 2.2.1

Simplify

3 (0) - 4 y

$3 (0) - 4 y$ .

Tap for more steps...

Step 2.2.1.1

Multiply

3

$3$ by

0

$0$ .

0 - 4 y = 12

$0 - 4 y = 12$

Step 2.2.1.2

Subtract

4 y

$4 y$ from

0

$0$ .

- 4 y = 12

$- 4 y = 12$

- 4 y = 12

$- 4 y = 12$

Step 2.2.2

Divide each term in

- 4 y = 12

$- 4 y = 12$ by

- 4

$- 4$ and simplify.

Tap for more steps...

Step 2.2.2.1

Divide each term in

- 4 y = 12

$- 4 y = 12$ by

- 4

$- 4$ .

\frac{- 4 y}{- 4} = \frac{12}{- 4}

$\frac{- 4 y}{- 4} = \frac{12}{- 4}$

Step 2.2.2.2

Simplify the left side.

Tap for more steps...

Step 2.2.2.2.1

Cancel the common factor of

- 4

$- 4$ .

Tap for more steps...

Step 2.2.2.2.1.1

Cancel the common factor.

\frac{- 4 y}{- 4} = \frac{12}{- 4}

$\frac{- 4 y}{- 4} = \frac{12}{- 4}$

Step 2.2.2.2.1.2

Divide

y

$y$ by

1

$1$ .

y = \frac{12}{- 4}

$y = \frac{12}{- 4}$

y = \frac{12}{- 4}

$y = \frac{12}{- 4}$

y = \frac{12}{- 4}

$y = \frac{12}{- 4}$

Step 2.2.2.3

Simplify the right side.

Tap for more steps...

Step 2.2.2.3.1

Divide

12

$12$ by

- 4

$- 4$ .

y = - 3

$y = - 3$

y = - 3

$y = - 3$

y = - 3

$y = - 3$

y = - 3

$y = - 3$

Step 2.3

y-intercept(s) in point form.

y-intercept(s):

(0, - 3)

$(0, - 3)$

y-intercept(s):

(0, - 3)

$(0, - 3)$

Step 3

List the intersections.

x-intercept(s):

(4, 0)

$(4, 0)$

y-intercept(s):

(0, - 3)

$(0, - 3)$

Step 4

[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$