Determine is a linear equation, if so write it in standard form

3x=5y

7y=2x+5x

To determine if an equation is linear, we need to check if all variables have a degree of 1. In the given equation, we have 3x = 5y, where both x and y have a degree of 1. Therefore, it is a linear equation.

To write it in standard form, we need to rearrange the equation so that the variables are on the left side and the constant is on the right side, with the coefficients being integers. The standard form of a linear equation is Ax + By = C.

Starting with 3x = 5y, we can rearrange it to get all terms on the left side:

3x - 5y = 0

Now, we can multiply both sides of the equation by -1 to make the x coefficient positive:

-3x + 5y = 0

This is the equation in standard form, where A = -3, B = 5, and C = 0.

Moving on to the next equation, 7y = 2x + 5x, we can simplify it:

7y = 7x

Both x and y have a degree of 1, so it is a linear equation.

To write it in standard form, we rearrange the equation:

-7x + 7y = 0

Now, we have it in standard form with A = -7, B = 7, and C = 0.