liizzyliizz 3 years ago Solve using elimination. 5x + 2y = 7 10x + 4y = 14 ok so I am reteaching myself algebra 2, and I was doing this, would there be no solution? I am not sure If I did this correct.

1. jim_thompson5910

let z = 5x+2y

2. jim_thompson5910

double both sides 2z = 2(5x+2y) 2z = 10x+4y

3. jim_thompson5910

so if 5x + 2y = 7 10x + 4y = 14 then we can also say z = 7 2z = 14 where z = 5x+2y

4. jim_thompson5910

but....what happens when we solve 2z = 14 for z?

5. liizzyliizz

I am not sure If I am thinking about this in the correct way, but technically wouldn't z would = 7. and we already know that. So I am a bit lost now, with where you're going with this.

6. jim_thompson5910

2z = 14 ---> z = 7 but z = 7 in the first equation

7. jim_thompson5910

so no matter what happens, we're going to get z = 7

8. jim_thompson5910

so because z = 5x+2y, this means that 5x+2y = 7 and this applies to both equations because the two are really the same equation

9. Mertsj

The problem says to solve by elimination so multiply the first equation by -2 and then add the two equations. You will get the true statement 0=0 which tells you that there is an infinite number of solutions.

10. liizzyliizz

oh ok, I got the 0=0 but I wasnt sure if that meant infinite or no solutions. which is why I said no solutions. Ahh thank you for that clarification.

11. Mertsj

If you got a nonsense statement such as 0 = 3, that would indicate no solution.

12. liizzyliizz

that makes more sense, I feel so silly now for confusing that.