Calculus Examples

$2 x - y = 4$ , $- 2 x + y = 4$

Step 1

Solve by substitution to find the intersection between the curves.

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Step 1.1

Add $2 x$ to both sides of the equation.

$y = 4 + 2 x$

$2 x - y = 4$

Step 1.2

Replace all occurrences of $y$ with $4 + 2 x$ in each equation.

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Step 1.2.1

Replace all occurrences of $y$ in $2 x - y = 4$ with $4 + 2 x$ .

$2 x - (4 + 2 x) = 4$

$y = 4 + 2 x$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Simplify $2 x - (4 + 2 x)$ .

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Step 1.2.2.1.1

Simplify each term.

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Step 1.2.2.1.1.1

Apply the distributive property.

$2 x - 1 \cdot 4 - (2 x) = 4$

$y = 4 + 2 x$

Step 1.2.2.1.1.2

Multiply $- 1$ by $4$ .

$2 x - 4 - (2 x) = 4$

$y = 4 + 2 x$

Step 1.2.2.1.1.3

Multiply $2$ by $- 1$ .

$2 x - 4 - 2 x = 4$

$y = 4 + 2 x$

$2 x - 4 - 2 x = 4$

$y = 4 + 2 x$

Step 1.2.2.1.2

Combine the opposite terms in $2 x - 4 - 2 x$ .

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Step 1.2.2.1.2.1

Subtract $2 x$ from $2 x$ .

$0 - 4 = 4$

$y = 4 + 2 x$

Step 1.2.2.1.2.2

Subtract $4$ from $0$ .

$- 4 = 4$

$y = 4 + 2 x$

$- 4 = 4$

$y = 4 + 2 x$

$- 4 = 4$

$y = 4 + 2 x$

$- 4 = 4$

$y = 4 + 2 x$

$- 4 = 4$

$y = 4 + 2 x$

Step 1.3

Since $- 4 = 4$ is not true, there is no solution.

No solution

Step 2

The area between the given curves is unbounded.

Unbounded area

Step 3