To determine if a linear equation is in standard form, we need to write the equation in the form of:
Ax + By = C
Let's check each equation:
1. 3x = 5y
To convert this equation into standard form, move all the terms to the left side of the equation:
3x - 5y = 0
So, the equation 3x = 5y is in standard form.
2. 7y = 2x + 5x
Combine the x terms on the right side:
7y = 7x
Now, subtract 7x from both sides to bring the terms to the left side:
-7x + 7y = 0
So, the equation 7y = 2x + 5x is also in standard form.
3. 3/x + 4/y = 2
To put this equation in standard form, we need to eliminate the fractions. Multiply the entire equation by x and y to get rid of the denominators:
3xy + 4x = 2xy
Now, move all the terms to one side:
3xy - 2xy + 4x = 0
Combine like terms:
xy + 4x = 0
This equation is not in standard form since it contains the product of x and y. To be in standard form, the equation should only have x and y as separate terms without any product.
To summarize:
1. 3x = 5y is already in standard form.
2. 7y = 2x + 5x can be written as -7x + 7y = 0 (standard form).
3. 3/x + 4/y = 2 is not in standard form.