How To Solve 3x -2y=15? The Steps To Solving The Problem


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In these types of problems you are trying to find x AND y. Don't worry, I will show this to you step-by-step. :)

Well, in 3x - 2y = 15, the first thing you must do is decide which variable you want to solve first. I usually go with x, so let's solve x first. When solving for a certain variable in these types of problems, it is beneficial to put them on one side of the equation and other number terms on the other side of the equation. Like so:

3x = 2y + 15

I simply added 2y to both sides so that 3x would be left alone on the left side of the equation. Now, to finally find x, you must divide both sides by three since 3x contains a three in it.

x = 2y/3 + 5
Now, you just leave x as is. Now look at your original problem. 3x - 2y = 15. Plug in your resultant to the x variable and then check to see that your resultant for x is true. So you plug in 2y/3 + 5 to the x variable.

3(2y/3 + 5) - 2y = 15

Then after that, you must distribute the three to 2y/3 and to five, and simplify the problem down.

2y + 15 - 2y = 15
15 = 15

Therefore, the resultant for the x variable was true, x does equal 2y/3 + 5. Now, you must solve for y. Look at your original problem. 3x - 2y = 15. Just do the same basic steps as you did to solve x, except you are now solving for y. So, subtract 3x from both sides, and then divide both sides by -2 so that the left side of the equation is just y.

3x - 3x - 2y = 15 - 3x
-2y = 15 - 3x
-2y/-2 = (15 - 3x)/2
y = -7.5 + 1.5x

You have now found the answer to y. Just like for when you were solving for x, you plug in the resultant you got for y into the original problem, 3x - 2y = 15, and then check to see if that is truly your answer.

3x - 2(-7.5 + 1.5x) = 15

You must distribute the negative two to the -7.5 + 1.5x, and then just simplify the problem down.

3x + 15 - 3x = 15
15 = 15

Okay! So the resultant for y, -7.5 + 1.5x, was also true. Therefore, x = 2y/3 + 5 and y = -7.5 + 1.5x.

I hope I did not confuse you. :p If you need anymore help with math, or if you got confused somewhere in this problem, just contact me at [email protected].

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