Let x be the number of questions he answered correctly, y the number of questions he answered incorrectly. Then his score is 10x- 5y= 150. An obvious first step is to divide through by 5 to get 2x- y= 30. As dokrbb says, that is a single equation with two variables. In general we could choose any number for x and calculate the corresponding y but because these are "numbers of questions", x and y must be non-negative integers so this is a "Diophantine" equation and we can find a formula for the possible solutions.

+ First note that if x= y= 30, we have 2(30)- 30= 30 so x= 30, y= 30 is one answer. But we can see that x= 30+ n, y= 30+ 2n is also a solution for any n: 2(30+ n)- (30+ 2n)= 60+ 2n- 30- 2n= 30. Since y cannot be negative, n cannot be smaller than -15. So we have an infinite number of solutions, x= 30+ n, y= 30+ 2n for \(\displaystyle n/ge -15\) or, if you prefer, x= 15+ n, y= 2n for \(\displaystyle n\ge 0\).