Algebra Examples

5 x + 2 y = 10

$5 x + 2 y = 10$

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

$x$ .

5 x + 2 (0) = 10

$5 x + 2 (0) = 10$

Step 1.2

Solve the equation.

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Step 1.2.1

Simplify

5 x + 2 (0)

$5 x + 2 (0)$ .

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Step 1.2.1.1

Multiply

2

$2$ by

0

$0$ .

5 x + 0 = 10

$5 x + 0 = 10$

Step 1.2.1.2

Add

5 x

$5 x$ and

0

$0$ .

5 x = 10

$5 x = 10$

5 x = 10

$5 x = 10$

Step 1.2.2

Divide each term in

5 x = 10

$5 x = 10$ by

5

$5$ and simplify.

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Step 1.2.2.1

Divide each term in

5 x = 10

$5 x = 10$ by

5

$5$ .

\frac{5 x}{5} = \frac{10}{5}

$\frac{5 x}{5} = \frac{10}{5}$

Step 1.2.2.2

Simplify the left side.

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Step 1.2.2.2.1

Cancel the common factor of

5

$5$ .

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Step 1.2.2.2.1.1

Cancel the common factor.

$\frac{5 x}{5} = \frac{10}{5}$

Step 1.2.2.2.1.2

Divide

$x$ by

$1$ .

$x = \frac{10}{5}$

$x = \frac{10}{5}$

$x = \frac{10}{5}$

Step 1.2.2.3

Simplify the right side.

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Step 1.2.2.3.1

Divide

$10$ by

$5$ .

$x = 2$

$x = 2$

$x = 2$

$x = 2$

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

$y$ .

$5 (0) + 2 y = 10$

Step 2.2

Solve the equation.

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Step 2.2.1

Simplify

$5 (0) + 2 y$ .

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Step 2.2.1.1

Multiply

$5$ by

$0$ .

$0 + 2 y = 10$

Step 2.2.1.2

Add

$0$ and

$2 y$ .

$2 y = 10$

$2 y = 10$

Step 2.2.2

Divide each term in

$2 y = 10$ by

$2$ and simplify.

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Step 2.2.2.1

Divide each term in

$2 y = 10$ by

$2$ .

$\frac{2 y}{2} = \frac{10}{2}$

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.

$\frac{2 y}{2} = \frac{10}{2}$

Step 2.2.2.2.1.2

Divide

$y$ by

$1$ .

$y = \frac{10}{2}$

$y = \frac{10}{2}$

$y = \frac{10}{2}$

Step 2.2.2.3

Simplify the right side.

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Step 2.2.2.3.1

Divide

$10$ by

$2$ .

$y = 5$

$y = 5$

$y = 5$

$y = 5$

Step 2.3

y-intercept(s) in point form.

y-intercept(s):

$(0, 5)$

y-intercept(s):

$(0, 5)$

Step 3

List the intersections.

x-intercept(s):

$(2, 0)$

y-intercept(s):

$(0, 5)$

Step 4

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