I need help with solving for y and x, for example in a problem like

3/2x- 2y= 20
how do you solve for y or x
how do know what to subtract
I need to know how to do this in order to do substitution
please any help will be appreciated, thanx

Add 2y to both sides.

subtract 20 from both sides, and finally, divide both sides by 2.

With only one equation, all you can do is express x in terms of y or y in terms of x. You cannot solve for both simultaneously unless you have a second independent equation.

For y in terms of x, add 2y - 20 to both sides and you get
(3/2)x -20 = 2y
Now divide both sides by 2 and you end up with
y = (3/4)x - 10

thanks for the help

To solve for y and x in an equation like 3/2x - 2y = 20, you can use a method called solving by elimination. Here's how you can do it:

1. Start by rearranging the equation in standard form, which means putting the x and y terms on one side and the constant on the other side:
3/2x - 2y = 20
3/2x - 20 = 2y

2. Now, to eliminate one variable (either x or y), you need to multiply each equation by a value such that the coefficients of either x or y will be the same magnitude when added or subtracted. In this case, we can eliminate the x-term by multiplying the first equation by 2 and the second equation by 3:
2 * (3/2x - 2y) = 2 * 20 --> 3x - 4y = 40
3 * (3/2x - 20) = 3 * 2y --> 9/2x - 60 = 6y

3. Now, by multiplying through by 2, we can eliminate the fraction in the second equation:
2 * (9/2x - 60) = 2 * 6y --> 9x - 120 = 12y

4. Now we have two equations in terms of y:
3x - 4y = 40
9x - 12y = 120

5. Next, we can choose any method to solve the system of equations, such as substitution or elimination. Since you mentioned substitution, let's use that method. Rearrange the first equation to solve for x:
3x = 4y + 40 --> x = (4y + 40)/3

6. Substitute the expression for x into the second equation:
9((4y + 40)/3) - 12y = 120

7. Simplify and solve for y:
(12y + 120) - 12y = 120
120 = 120

8. Since the equation simplifies to a true statement, 120 = 120, this means that the system of equations is dependent. In other words, any value of y will satisfy the original equation. Therefore, there are infinitely many solutions for y.

9. To find the corresponding values for x, substitute the value of y back into one of the original equations. For example, substituting y = 2 into the first equation gives us:
3/2x - 2(2) = 20
3/2x - 4 = 20
3/2x = 24
x = 16

10. So, one possible solution is x = 16 and y = 2. But remember, since this is a dependent system, there are infinitely many solutions, and each corresponding pair of x and y values will satisfy the equation.

In summary, to solve for y and x in an equation, you can use the method of solving by elimination, substitution, or any other appropriate method. The key is to rearrange the equation, eliminate one variable, and then solve for the remaining variable.