00:01
In this video, we're going to be solving this following system of equations.
00:05
Our approach is going to be to take the simpler of the two equations and solve for one variable using the substitution method.
00:13
So in this second equation, let's start off by adding three to both sides to get that x times y equals three.
00:21
Because this right -hand side is not zero, we can conclude immediately that x itself cannot be zero and y cannot.
00:30
Be 0.
00:31
This allows us to divide by the variable x and obtain that y equals 3 divide by x.
00:39
This quantity is not undefined since we're disallowing x to be 0 and this lets us to be certain that we have not missed any solutions when we go to solve this equation.
00:49
So for our next step we're going to substitute in the value for y here and here.
00:56
So let's write 2x plus 5 times a placeholder for y plus 7x times another placeholder for y equals 8 and we just found that y equals 3 over x so we'll place it into these two positions analyzing this equation we see that x's cancel on this term so we just pick up a 21 and now the equation reads 2x plus 15 divide by x plus 21 is equal to 8 the most pressing issue about this equation so far is that denominator involving x.
01:38
So we'll take a step to multiply the left side and the right side by x in order to clear that denominator.
01:46
We obtain 2x squared plus 15, since x cancels out, plus 21x, equals 8x.
01:57
Now for the next steps, we're going to consolidate all of the terms to one side so that we can obtain zero on the opposite side.
02:08
Let's subtract 8x from both sides so that we'll get 2x squared.
02:13
21x minus 8x gives us positive 13x and i'll add 15 equals 0.
02:22
So this is now the equation that we must solve.
02:25
In solving this equation, let's attempt a factorization first.
02:30
So we'll lay down two sets of parentheses, multiplying each other.
02:34
2x squared can be broken down as a 2x times x.
02:39
Due to this sign and this sign, both being positives, we know that the middle signs are also both positive...