Kristy, It depends on whether you are solving for x or for y. Whatever variable you are solving for you want to isolate it on one side. Unless you know the values for x or y, you will have an answer with one of the variables in it. For example, to solve for x: 2x-3y=10; first move the 3y to the other side so, 2x= 3y + 10- you have to add 3y to cancel it from a negative (-3y). Then, you have to get rid of the 2 multiplied (next to the x). Since it's multiplication, you'll have to divide. Remember a key rule: whatever you do to one side, you have to do to the other. So, divide the 2x by 2 and then divide 3y + 10 by 2. The 2 will be cancelled by the x and your answer will have to remain x = 3y + 10 divided by 2/ The answers stays this way because you do not know the value of y to do any more. Hope this helps! Sincerely, Shannon

1)2x-3y = 10

   -2x         -2x (subtract 2x from both sides to isolate variables)

2)(-1/3)-3y = [10 - 2x](-1/3) Multiply both sides by -1/3 to isolate the y-variable

 

3) y = 2x/3 - 10/3

This is the slope-intercept form of an equation of a line with slope 2/3 and intercepts the y-axis at (0,-10/3).

Kristy,

Yes 2x-3y=10 is an equation and yes you can solve for x or y as stated by Shannon and Jane; however, I encourage you to represent the equation as a line on a graph.  Do this by plotting the solution for y as stated... 

y=2/3x - 10/3

Once you have done that, you should be able to see that both expressions,

y=2/3x - 10/3   or   x=3/2y + 5 

represent the same line, or in other words these two expressions are equivalent.

2x - 3y = 10 + 3y + 3y (add 3y to both sides) 2x = 10 + 3y 2x/2 = 10/2 + 3y/2 (divide each coefficient by 2 to isolate x) X = 5 + 3/2 y (this is the SIMPLIFIED answer for X) ---or if you are solving for 'y'--- 2x -3y = 10 - 2x - 2x (minus 2x from both sides of the equation) -3y = 10 - 2x (rewrite the equation for clarity) 3y = -10 + 2x (multiply both sides by -1 to make your y positive) 3y = 2x - 10 (rewrite for clarity) y = 2/3x - 10/3 (divide both sides by 3 to isolate y.) This is the SIMPLIFIED answer for Y.