You may want to review solving ordinary linear equations first.

Sometimes, linear equations have more than one variable. That's okay; you just need to know which one we're interested in. When you're given a problem, it should say to solve “for” some variable. If you're told to solve 3x + 4y − 4 = 2x − 1 for y, say, then that means that you need to find what values of y make the equation right. The answer will in general depend on x. That's okay — you're allowed to have letters in your answer. The one letter that you aren't allowed to have in your answer is the letter you were asked to solve for.

You do these problems the same way you solved linear equations with just one variable in them, except you treat the other letters the same as you would numbers. You might have to simplify your answer at the end. In our example, both sides are already simplified, and y (the letter we're solving for) is only on one side. However, there's stuff being added and subtracted on the side where y is. So we need to subtract 3x from both sides and to add 4 to both sides. This gives us 4y = −x + 3. Now we divide both sides by 4 (the number y is being multiplied by) and get y = (−x + 3) / 4, which simplifies to −(1 ⁄ 4)x + 3 ⁄ 4, so that's our answer.