Calculus Examples

$y = 3 x - 4$ , $y = x$

Step 1

Solve by substitution to find the intersection between the curves.

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Step 1.1

Eliminate the equal sides of each equation and combine.

$3 x - 4 = x$

Step 1.2

Solve $3 x - 4 = x$ for $x$ .

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Step 1.2.1

Move all terms containing $x$ to the left side of the equation.

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Step 1.2.1.1

Subtract $x$ from both sides of the equation.

$3 x - 4 - x = 0$

Step 1.2.1.2

Subtract $x$ from $3 x$ .

$2 x - 4 = 0$

Step 1.2.2

Add $4$ to both sides of the equation.

$2 x = 4$

Step 1.2.3

Divide each term in $2 x = 4$ by $2$ and simplify.

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Step 1.2.3.1

Divide each term in $2 x = 4$ by $2$ .

$\frac{2 x}{2} = \frac{4}{2}$

Step 1.2.3.2

Simplify the left side.

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Step 1.2.3.2.1

Cancel the common factor of $2$ .

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Step 1.2.3.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{4}{2}$

Step 1.2.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{4}{2}$

Step 1.2.3.3

Simplify the right side.

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Step 1.2.3.3.1

Divide $4$ by $2$ .

$x = 2$

Step 1.3

Evaluate $y$ when $x = 2$ .

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Step 1.3.1

Substitute $2$ for $x$ .

$y = 2$

Step 1.3.2

Remove parentheses.

$y = 2$

Step 1.4

The solution to the system is the complete set of ordered pairs that are valid solutions.

$(2, 2)$

Step 2

The area between the given curves is unbounded.

Unbounded area

Step 3