Solve 2x+3y=5x-y - ScanMath

Question

Function

$Find the x -intercept/zero$

Find the y-intercept

Find the slope

x = 0

Evaluate

2 x + 3 y = 5 x - y

To find the x -intercept,set y =0

2 x + 3 \times 0 = 5 x - 0

Any expression multiplied by 0 equals 0

2 x + 0 = 5 x - 0

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

2 x = 5 x - 0

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

2 x = 5 x

Add or subtract both sides

2 x - 5 x = 0

Subtract the terms

More Steps

Evaluate

2 x - 5 x

Collect like terms by calculating the sum or difference of their coefficients

(2 - 5) x

Subtract the numbers

- 3 x

- 3 x = 0

Change the signs on both sides of the equation

3 x = 0

Solution

x = 0

Show Solution

Solve the equation

$Solve for x$

$Solve for y$

x = \frac{4 y}{3}

Evaluate

2 x + 3 y = 5 x - y

Move the expression to the left side

2 x + 3 y - 5 x = - y

Move the expression to the right side

2 x - 5 x = - y - 3 y

Add and subtract

More Steps

Evaluate

2 x - 5 x

Collect like terms by calculating the sum or difference of their coefficients

(2 - 5) x

Subtract the numbers

- 3 x

- 3 x = - y - 3 y

Add and subtract

More Steps

Evaluate

- y - 3 y

Factor the expression

(- 1 - 3) y

Subtract the terms

- 4 y

- 3 x = - 4 y

Change the signs on both sides of the equation

3 x = 4 y

Divide both sides

\frac{3 x}{3} = \frac{4 y}{3}

Solution

x = \frac{4 y}{3}

Show Solution

Testing for symmetry

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Symmetry with respect to the origin

Evaluate

2 x + 3 y = 5 x - y

To test if the graph of 2 x + 3 y = 5 x - y is symmetry with respect to the origin,substitute -x for x and -y for y

2 (- x) + 3 (- y) = 5 (- x) - (- y)

Evaluate

More Steps

Evaluate

2 (- x) + 3 (- y)

Multiply the numbers

- 2 x + 3 (- y)

Multiply the numbers

- 2 x - 3 y

- 2 x - 3 y = 5 (- x) - (- y)

Evaluate

More Steps

Evaluate

5 (- x) - (- y)

Multiply the numbers

- 5 x - (- y)

Rewrite the expression

- 5 x + y

- 2 x - 3 y = - 5 x + y

Solution

Symmetry with respect to the origin

Show Solution

Rewrite the equation

Rewrite in polar form

Rewrite in standard form

Rewrite in slope-intercept form

r = 0 θ = arctan (\frac{3}{4}) + kπ, k \in Z

Evaluate

2 x + 3 y = 5 x - y

Move the expression to the left side

- 3 x + 4 y = 0

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

- 3 cos (θ) \times r + 4 sin (θ) \times r = 0

Factor the expression

(- 3 cos (θ) + 4 sin (θ)) r = 0

Separate into possible cases

r = 0 - 3 cos (θ) + 4 sin (θ) = 0

Solution

More Steps

Evaluate

- 3 cos (θ) + 4 sin (θ) = 0

Move the expression to the right side

4 sin (θ) = 0 - (- 3 cos (θ))

Subtract the terms

4 sin (θ) = 3 cos (θ)

Divide both sides

\frac{4 sin ( θ )}{cos ( θ )} = 3

Divide the terms

More Steps

Evaluate

\frac{4 sin ( θ )}{cos ( θ )}

Rewrite the expression

4 cos^{- 1} (θ) sin (θ)

Rewrite the expression

4 tan (θ)

4 tan (θ) = 3

Multiply both sides of the equation by \frac{1}{4}

4 tan (θ) \times \frac{1}{4} = 3 \times \frac{1}{4}

Calculate

tan (θ) = 3 \times \frac{1}{4}

Multiply the numbers

tan (θ) = \frac{3}{4}

Use the inverse trigonometric function

θ = arctan (\frac{3}{4})

Add the period of kπ, k \in Z to find all solutions

θ = arctan (\frac{3}{4}) + kπ, k \in Z

r = 0 θ = arctan (\frac{3}{4}) + kπ, k \in Z

Show Solution

Find the first derivative

$Find the derivative with respect to x$

$Find the derivative with respect to y$

\frac{d y}{d x} = \frac{3}{4}

Calculate

2 x + 3 y = 5 x - y

Take the derivative of both sides

\frac{d}{d x} (2 x + 3 y) = \frac{d}{d x} (5 x - y)

Calculate the derivative

More Steps

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

More Steps

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

More Steps

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} (5 x - y)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (5 x - y)

Use differentiation rules

\frac{d}{d x} (5 x) + \frac{d}{d x} (- y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (5 x)

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

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

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

5 \times 1

Any expression multiplied by 1 remains the same

5

5 + \frac{d}{d x} (- y)

Evaluate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

- \frac{d y}{d x}

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

2 + 3 \frac{d y}{d x} = 5 - \frac{d y}{d x}

Move the expression to the left side

2 + 3 \frac{d y}{d x} + \frac{d y}{d x} = 5

Move the expression to the right side

3 \frac{d y}{d x} + \frac{d y}{d x} = 5 - 2

Add and subtract

More Steps

Evaluate

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

Collect like terms by calculating the sum or difference of their coefficients

(3 + 1) \frac{d y}{d x}

Add the numbers

4 \frac{d y}{d x}

4 \frac{d y}{d x} = 5 - 2

Add and subtract

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

Divide both sides

\frac{4 \frac{d y}{d x}}{4} = \frac{3}{4}

Solution

\frac{d y}{d x} = \frac{3}{4}

Show Solution

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 = 5 x - y

Take the derivative of both sides

\frac{d}{d x} (2 x + 3 y) = \frac{d}{d x} (5 x - y)

Calculate the derivative

More Steps

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

More Steps

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

More Steps

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} (5 x - y)

Calculate the derivative

More Steps

Evaluate

\frac{d}{d x} (5 x - y)

Use differentiation rules

\frac{d}{d x} (5 x) + \frac{d}{d x} (- y)

Evaluate the derivative

More Steps

Evaluate

\frac{d}{d x} (5 x)

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

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

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

5 \times 1

Any expression multiplied by 1 remains the same

5

5 + \frac{d}{d x} (- y)

Evaluate the derivative

More Steps

Evaluate

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

Use differentiation rules

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

Evaluate the derivative

- \frac{d y}{d x}

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

2 + 3 \frac{d y}{d x} = 5 - \frac{d y}{d x}

Move the expression to the left side

2 + 3 \frac{d y}{d x} + \frac{d y}{d x} = 5

Move the expression to the right side

3 \frac{d y}{d x} + \frac{d y}{d x} = 5 - 2

Add and subtract

More Steps

Evaluate

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

Collect like terms by calculating the sum or difference of their coefficients

(3 + 1) \frac{d y}{d x}

Add the numbers

4 \frac{d y}{d x}

4 \frac{d y}{d x} = 5 - 2

Add and subtract

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

Divide both sides

\frac{4 \frac{d y}{d x}}{4} = \frac{3}{4}

Divide the numbers

\frac{d y}{d x} = \frac{3}{4}

Take the derivative of both sides

\frac{d}{d x} (\frac{d y}{d x}) = \frac{d}{d x} (\frac{3}{4})

Calculate the derivative

\frac{d ^{2} y}{d x ^{2}} = \frac{d}{d x} (\frac{3}{4})

Solution

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

Show Solution

2x+3y=5x Y

Function

$Find the x -intercept/zero$

Find the y-intercept

Find the slope

Solve the equation

$Solve for x$

$Solve for y$

Testing for symmetry

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Rewrite the equation

Rewrite in polar form

Rewrite in standard form

Rewrite in slope-intercept form

Find the first derivative

$Find the derivative with respect to x$

$Find the derivative with respect to y$

Find the second derivative

$Find the second derivative with respect to x$

$Find the second derivative with respect to y$

Graph

2x+3y=5x Y

Function

Find the x-intercept/zero

Find the y-intercept

Find the slope

Solve the equation

Solve for x

Solve for y

Testing for symmetry

Testing for symmetry about the origin

Testing for symmetry about the x-axis

Testing for symmetry about the y-axis

Rewrite the equation

Rewrite in polar form

Rewrite in standard form

Rewrite in slope-intercept form

Find the first derivative

Find the derivative with respect to x

Find the derivative with respect to y

Find the second derivative

Find the second derivative with respect to x

Find the second derivative with respect to y

Graph

$Find the x -intercept/zero$

$Solve for x$

$Solve for y$

$Find the derivative with respect to x$

$Find the derivative with respect to y$

$Find the second derivative with respect to x$

$Find the second derivative with respect to y$