When doing this problem, the first thing I would recommend is to get rid of the decimals. If I multiply everything through by 100, I get five X + 25 Y equaling 1100. I can see that all of those numbers are then divisible by 5 S X + 5 Y, equaling 220. Now for the other equation, I'm going to multiply everything through by 5 S or by 100. Sorry, fifteen X + 5 Y equaling 1200. I'm going to divide everything through by a 5 three X + y equaling 5 into 12 to 240. So now I have two new equations. We have X + 5 Y equaling 220 and three X + y equal to 40. So let's say we want to get rid of the X's to start. Take that top equation, multiply it all through by -3 negative three X -, 15 Y equal -660. The other equation we're going to leave the same because it already was a 3X. When we add those, the three XS go away, we get a -14 Y equaling -420. If we divide, we get -420 / -14 negative divided by negative is positive. They're both Even. So we get 210 / 7, and seven goes into 21 three times. So seven goes into 2137 goes into 00, so 30. If we go back to those two simplified equations and think about getting rid of the YS this time we're going to take the second equation and multiply it through by a -5. So the first equation is going to stay the same. The second equation is going to turn into -15 X -5 Y equaling -0 zero to 1012 hundred. So when we add these we get -14 X. The YS go away this time and we get -980. So divide each side by -14 a negative divided by a negative is a positive. They're both even. So 490 / 7, and then seven evenly goes into 49, so 7 and 49 is 7/7 into 00. So we get a point of 70, 30. These are consistent because there's a solution. They're independent because they're two separate lines.