Algebra Examples

3 x - 2 y = 6

$3 x - 2 y = 6$

Step 1

Find the x-intercepts.

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Step 1.1

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

0

$0$ for

y

$y$ and solve for

x

$x$ .

3 x - 2 \cdot 0 = 6

$3 x - 2 \cdot 0 = 6$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify

3 x - 2 \cdot 0

$3 x - 2 \cdot 0$ .

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Step 1.2.1.1

Multiply

- 2

$- 2$ by

0

$0$ .

3 x + 0 = 6

$3 x + 0 = 6$

Step 1.2.1.2

Add

3 x

$3 x$ and

0

$0$ .

3 x = 6

$3 x = 6$

3 x = 6

$3 x = 6$

Step 1.2.2

Divide each term in

3 x = 6

$3 x = 6$ by

3

$3$ and simplify.

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Step 1.2.2.1

Divide each term in

3 x = 6

$3 x = 6$ by

3

$3$ .

\frac{3 x}{3} = \frac{6}{3}

$\frac{3 x}{3} = \frac{6}{3}$

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Cancel the common factor of

3

$3$ .

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Step 1.2.2.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{6}{3}$

Step 1.2.2.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{6}{3}$

$x = \frac{6}{3}$

$x = \frac{6}{3}$

Step 1.2.2.3

Simplify the right side.

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Step 1.2.2.3.1

Divide

$6$ by

$3$ .

$x = 2$

$x = 2$

$x = 2$

$x = 2$

Step 1.3

x-intercept(s) in point form.

x-intercept(s):

$(2, 0)$

x-intercept(s):

$(2, 0)$

Step 2

Find the y-intercepts.

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Step 2.1

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

$0$ for

$x$ and solve for

$y$ .

$3 (0) - 2 y = 6$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify

$3 (0) - 2 y$ .

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Step 2.2.1.1

Multiply

$3$ by

$0$ .

$0 - 2 y = 6$

Step 2.2.1.2

Subtract

$2 y$ from

$0$ .

$- 2 y = 6$

$- 2 y = 6$

Step 2.2.2

Divide each term in

$- 2 y = 6$ by

$- 2$ and simplify.

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Step 2.2.2.1

Divide each term in

$- 2 y = 6$ by

$- 2$ .

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

Step 2.2.2.2

Simplify the left side.

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Step 2.2.2.2.1

Cancel the common factor of

$- 2$ .

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Step 2.2.2.2.1.1

Cancel the common factor.

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

Step 2.2.2.2.1.2

Divide

$y$ by

$1$ .

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

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

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

Step 2.2.2.3

Simplify the right side.

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Step 2.2.2.3.1

Divide

$6$ by

$- 2$ .

$y = - 3$

$y = - 3$

$y = - 3$

$y = - 3$

Step 2.3

y-intercept(s) in point form.

y-intercept(s):

$(0, - 3)$

y-intercept(s):

$(0, - 3)$

Step 3

List the intersections.

x-intercept(s):

$(2, 0)$

y-intercept(s):

$(0, - 3)$

Step 4

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