00:01
Okay, the easiest way to do this, solve this system is to solve by substitution.
00:10
So to do substitution, we need to get the bottom one equal to either x or y.
00:15
So it's going to be easiest to get it equal to x.
00:18
So we're going to add y to both sides.
00:21
So that gives us x equals 3 plus y.
00:25
Now let's plug this in for x.
00:28
So x squared.
00:30
So 3 plus y squared.
00:34
Minus six times three plus y times y plus nine y squared equals one i already reword redo this i want to have this six y times that because it'll make it a little bit easier for us all right so y plus three square so y squared plus six y plus nine all right so that's this factored out i multiply it out so that's going to give us negative 18 y minus 6 y squared plus 9 y squared equals 1 now it's combined our like terms so we have y squared minus 6 y that gives us 5 negative 5 y plus 9 y that gives us 4 y squared all this cancels out now i have 6 minus 18 so that's going to give me negative 12 12 y plus 9 equals 1 so let's subtract one on both sides so 4 y squared minus 12 y minus plus 8 equals 0 now all of these are divisible by 4 so let's divide everything by 4 so y squared plus 3 y plus minus 3 y i apologize minus 3y plus 2 equals 0.
02:19
So this is going to factor to y minus 2 times y minus 1 equals 0.
02:26
So our y values are 2 and 1.
02:31
Now that i have y values, i can plug those back in and solve for x.
02:37
So it's going to be easiest to do that in the second equation...