Calculus Examples

$x - 2 y = 0$ , $2 x - 3 y - 7 = 0$

Step 1

Solve by substitution to find the intersection between the curves.

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Step 1.1

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

$x = 2 y$

$2 x - 3 y - 7 = 0$

Step 1.2

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

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Step 1.2.1

Replace all occurrences of $x$ in $2 x - 3 y - 7 = 0$ with $2 y$ .

$2 (2 y) - 3 y - 7 = 0$

$x = 2 y$

Step 1.2.2

Simplify the left side.

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Step 1.2.2.1

Simplify $2 (2 y) - 3 y - 7$ .

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Step 1.2.2.1.1

Multiply $2$ by $2$ .

$4 y - 3 y - 7 = 0$

$x = 2 y$

Step 1.2.2.1.2

Subtract $3 y$ from $4 y$ .

$y - 7 = 0$

$x = 2 y$

$y - 7 = 0$

$x = 2 y$

$y - 7 = 0$

$x = 2 y$

$y - 7 = 0$

$x = 2 y$

Step 1.3

Add $7$ to both sides of the equation.

$y = 7$

$x = 2 y$

Step 1.4

Replace all occurrences of $y$ with $7$ in each equation.

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Step 1.4.1

Replace all occurrences of $y$ in $x = 2 y$ with $7$ .

$x = 2 (7)$

$y = 7$

Step 1.4.2

Simplify the right side.

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Step 1.4.2.1

Multiply $2$ by $7$ .

$x = 14$

$y = 7$

$x = 14$

$y = 7$

$x = 14$

$y = 7$

Step 1.5

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

$(14, 7)$

Step 2

The area between the given curves is unbounded.

Unbounded area

Step 3