In order to solve by elimination we first need to find a common multiple of the x or y values. Lets eliminate x. 7 and 2 (both the x values) can both go into 14 without having any left over. In order to turn 7 into 14 we must multiply it by 2. But in this case, we'll multiply the entire equation by 2 in order to not change its value. 14x-4y=34 Now lets do the same for the second equation. In order to turn 2 into 14, we can multiply it by 7, but again we need to multiply the entire equation by 7 so we dont change it's value. 14x+49y=511
Now that we have the same coefficient on both the x's we can get rid of them by subtracting the two equations.
14x+49y=511 14x-4y=34
53y=477 y=9
Now that we have the value for y we can plug it in and solve for x. 7x-2(9)=17 7x-18=17 7x=35 x=5
Since we are looking for the principal amount, then all we have to do is reverse the process of getting the amount of tax. In order to get the principal, you just have to divide 22 with 0.05. The answer is 440 so that is the principal amount you are looking for.