00:01
So in this problem we have two equations.
00:01
We have one -fifth x plus one half y equals 8.
00:10
Our second equation is just x plus 20 or x plus y equals 20.
00:17
Okay now what i like to do with all of these problems where you're solving for x and y is first just get rid of any fractions or decimals that might just become a hindrance or might leave you up into making a mistake.
00:29
So this first equation has a two and a five in denominators.
00:33
So if we just multiply that top equation by, 10 we can get an equivalent equation that would have the same solutions and it's the same line but with no longer any fractions or any decimals to speak of.
00:46
So 10 times 1 5x, that's just 2x, 10 times 1 half y, that's just 5 y, and 10 times 8 is 80.
00:59
So that's the new equation i'm going to use for my top equation.
01:03
Now using substitution, i want to use my bottom equation and i'm going to solve for x or y.
01:10
I'm going to solve for y just because that's what i'm kind of used to solving for, since it doesn't matter.
01:14
They're both just as easy.
01:16
So subtracting x from both sides, we have y equals negative x plus 20.
01:25
Okay, so now that we have an expression for y, we can plug that into our first equation.
01:30
So we're going to have 2x plus 5 times our y expression equals 80.
01:41
Our y expression was negative x plus 20.
01:47
So now we're just going to distribute and simplify a little bit...