00:01
This problem gives us two systems of linear equations and we want to solve both.
00:04
And it gives the hint to eliminate fractions first, so that's not an absolutely necessary step, but we'll do it just because that's what the hint was that they gave us.
00:13
I'm going to multiply by a 3 in the second equation for the first system, and we kind of get lucky here because the multiplying by 3 will actually give us an x value that will eliminate with the top x value, because the top equation will still stay 3x plus 2y equal to 4.
00:29
When we distribute this 3, we'll get negative 3x.
00:32
So those x will eliminate if we want to do elimination.
00:35
And then 3 times negative 2 thirds would be negative 6 thirds, which is negative 2y.
00:41
And then 3 times the negative 4 thirds will be negative 12 thirds, which is negative 4.
00:46
So now when we add through our columns for elimination, 3x plus negative 3x eliminates like we thought it would, but we also get 2i and negative 2i that eliminates as well.
00:55
So we get 0 equal to 4 plus negative 4, which is 0.
00:58
That's a true statement and since there are no more variables to solve for when the statement that results is true, that means there's infinitely many solutions.
01:08
And in your directions it said it's, if there's no solution, right, no solution, i don't know if that's what they want when you don't get an x, y point.
01:15
But when the statement that's left is true, it's infinitely many.
01:18
If it was something that wasn't true like 0 equals 1, that's never true.
01:21
That would be no solution...