Solve 2x-3y=6 - UpStudy

Question

2 x - 3 y = 6

Function

$Find the x -intercept/zero$
Find the y-intercept
Find the slope

x = 3

Evaluate

2 x - 3 y = 6

To find the x -intercept,set y =0

2 x - 3 \times 0 = 6

Any expression multiplied by 0 equals 0

2 x - 0 = 6

Removing 0 doesn't change the value,so remove it from the expression

2 x = 6

Divide both sides

\frac{2 x}{2} = \frac{6}{2}

Divide the numbers

x = \frac{6}{2}

Solution

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Evaluate

\frac{6}{2}

Reduce the numbers

\frac{3}{1}

Calculate

3

x = 3

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Solve the equation

$Solve for x$
$Solve for y$

x = \frac{6 + 3 y}{2}

Evaluate

2 x - 3 y = 6

Move the expression to the right-hand side and change its sign

2 x = 6 + 3 y

Divide both sides

\frac{2 x}{2} = \frac{6 + 3 y}{2}

Solution

x = \frac{6 + 3 y}{2}

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Testing for symmetry

Testing for symmetry about the origin
Testing for symmetry about the x-axis
Testing for symmetry about the y-axis

Not symmetry with respect to the origin

Evaluate

2 x - 3 y = 6

To test if the graph of 2 x - 3 y = 6 is symmetry with respect to the origin,substitute -x for x and -y for y

2 (- x) - 3 (- y) = 6

Evaluate

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Evaluate

2 (- x) - 3 (- y)

Multiply the numbers

- 2 x - 3 (- y)

Multiply the numbers

- 2 x - (- 3 y)

Rewrite the expression

- 2 x + 3 y

- 2 x + 3 y = 6

Solution

Not symmetry with respect to the origin

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Rewrite the equation

Rewrite in polar form
Rewrite in slope-intercept form

r = \frac{6}{2 c o s ( θ ) - 3 s i n ( θ )}

Evaluate

2 x - 3 y = 6

To convert the equation to polar coordinates,substitute x for r cos (θ) and y for r sin (θ)

2 cos (θ) \times r - 3 sin (θ) \times r = 6

Factor the expression

(2 cos (θ) - 3 sin (θ)) r = 6

Solution

r = \frac{6}{2 c o s ( θ ) - 3 s i n ( θ )}

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Find the first derivative

$Find the derivative with respect to x$
$Find the derivative with respect to y$

\frac{d y}{d x} = \frac{2}{3}

Calculate

2 x - 3 y = 6

Take the derivative of both sides

\frac{d}{d x} (2 x - 3 y) = \frac{d}{d x} (6)

Calculate the derivative

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Evaluate

\frac{d}{d x} (2 x - 3 y)

Use differentiation rules

\frac{d}{d x} (2 x) + \frac{d}{d x} (- 3 y)

Evaluate the derivative

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Evaluate

\frac{d}{d x} (2 x)

Use differentiation rule \frac{d}{d x} (c f (x)) = c \times \frac{d}{d x} (f (x))

2 \times \frac{d}{d x} (x)

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

2 \times 1

Any expression multiplied by 1 remains the same

2

2 + \frac{d}{d x} (- 3 y)

Evaluate the derivative

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Evaluate

\frac{d}{d x} (- 3 y)

Use differentiation rules

\frac{d}{d y} (- 3 y) \times \frac{d y}{d x}

Evaluate the derivative

- 3 \frac{d y}{d x}

2 - 3 \frac{d y}{d x}

2 - 3 \frac{d y}{d x} = \frac{d}{d x} (6)

Calculate the derivative

2 - 3 \frac{d y}{d x} = 0

Move the constant to the right-hand side and change its sign

- 3 \frac{d y}{d x} = 0 - 2

Removing 0 doesn't change the value,so remove it from the expression

- 3 \frac{d y}{d x} = - 2

Change the signs on both sides of the equation

3 \frac{d y}{d x} = 2

Divide both sides

\frac{3 \frac{d y}{d x}}{3} = \frac{2}{3}

Solution

\frac{d y}{d x} = \frac{2}{3}

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Find the second derivative

$Find the second derivative with respect to x$
$Find the second derivative with respect to y$

\frac{d ^{2} y}{d x ^{2}} = 0

Calculate

2 x - 3 y = 6

Take the derivative of both sides

\frac{d}{d x} (2 x - 3 y) = \frac{d}{d x} (6)

Calculate the derivative

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Evaluate

\frac{d}{d x} (2 x - 3 y)

Use differentiation rules

\frac{d}{d x} (2 x) + \frac{d}{d x} (- 3 y)

Evaluate the derivative

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Evaluate

\frac{d}{d x} (2 x)

Use differentiation rule \frac{d}{d x} (c f (x)) = c \times \frac{d}{d x} (f (x))

2 \times \frac{d}{d x} (x)

Use \frac{d}{d x} x^{n} = n x^{n - 1} to find derivative

2 \times 1

Any expression multiplied by 1 remains the same

2

2 + \frac{d}{d x} (- 3 y)

Evaluate the derivative

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Evaluate

\frac{d}{d x} (- 3 y)

Use differentiation rules

\frac{d}{d y} (- 3 y) \times \frac{d y}{d x}

Evaluate the derivative

- 3 \frac{d y}{d x}

2 - 3 \frac{d y}{d x}

2 - 3 \frac{d y}{d x} = \frac{d}{d x} (6)

Calculate the derivative

2 - 3 \frac{d y}{d x} = 0

Move the constant to the right-hand side and change its sign

- 3 \frac{d y}{d x} = 0 - 2

Removing 0 doesn't change the value,so remove it from the expression

- 3 \frac{d y}{d x} = - 2

Change the signs on both sides of the equation

3 \frac{d y}{d x} = 2

Divide both sides

\frac{3 \frac{d y}{d x}}{3} = \frac{2}{3}

Divide the numbers

\frac{d y}{d x} = \frac{2}{3}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (\frac{2}{3})

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (\frac{2}{3})

Solution

\frac{d ^{2} y}{d x ^{2}} = 0

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Graph