Elimination equation EXPLANATION WILL HELP THANKS

2. 2x + 7y = 1
x + 5y = 2

4. 9a - 2b = -8
-7a + 3b = 12

8. -5x + 3y = 6
x - y = 4

please show work I dont know how to do this my math teacher sucks and we having a test on it on friday :/ so hopefully youll explain everything on each question thanks

Ok, for each question, you have 2 equations. What you want to do is get an equal number of x's or y's in both equations, so you can cancel them out by the operations of arithmetic (usually subtraction) so you have only one variable to find. Once you've found that variable, just plug the value in in one of the equations and solve for x (or y). I'll do the first for you.

2x + 7y = 1
x + 5y = 2

Now, here we have 2x and 7y in the first equation, x and 5y in the second. Obviously, we have an unbalanced number of x's and y's in this situation. We could multiply the 1st equation by 5 and the 2nd by 7 in order to get 35y in both, but that's cumbersome and unnecessary. What we'll do instead is multiply the 2nd equation by 2 so we have 2x in both, like so:

2x + 7y = 1
2 * (x + 5y = 2) = 2x + 10y = 4

Now that we've balanced one of the variables, we can subtract the 1st equation from the second. A note to remember is that you can also subtract the 2nd from the 1st, if you like. I'm doing it this way to avoid dealing with negative numbers.

So now this is what we do:

(2x + 10y = 4) - (2x + 7y = 1)

Which equals

3y = 3
y = 1

Now we plug this value in the 1st equation:

2x + 7(1) = 1
2x + 7 = 1

Now we want to isolate the x terms. To do this, simply subtract 7, and the equation becomes

2x = -6
Dividing through by 2 will give you
x = -3

Now we'll put this value in the 2nd equation along with the y value:

-3 + 5(1) = 2
-3 + 5 = 2 (another way to think of this is to think of 5 - 3 --- That's what's really going on here)

-3 + 5 does indeed equal 2, so it checks out. x = -3 and y = 1. Now hopefully you should be able to do the rest by yourself.