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.

Question

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.

jim_thompson5910 · Answer

let z = 5x+2y

jim_thompson5910 · Answer

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

jim_thompson5910 · Answer

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

jim_thompson5910 · Answer

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

liizzyliizz · Answer

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.

jim_thompson5910 · Answer

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

jim_thompson5910 · Answer

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

jim_thompson5910 · Answer

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

mertsj · Answer

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.

liizzyliizz · Answer

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.

mertsj · Answer

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

liizzyliizz · Answer

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