2. Solve the system by the substitution method. xy= 10 x2+y2...

2. Solve the system by the substitution method. xy= 10 x\textsuperscript{2}+y\textsuperscript{2} = 29 Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The solution set is { (Type an ordered pair. Use a comma to separate answers as needed. Simplify your answer.) B. There is no solution.

Transcript

00:01 All right, so for this problem, we have a system of two exponentials, and we're going to solve the system.

00:08 We can do either elimination or substitution.

00:11 Both will work.

00:12 But if we examine this, we can tell that y is already solved for in the second equation.

00:18 So it'd be quite convenient to just substitute it into the first equation.

00:22 So let's do that to start.

00:24 So if we do that, we will get 9 to the power of x plus 2 minus 3 to the 1.

00:32 The x squared plus 2x power equals 0.

00:38 And what we can do here is we can actually rewrite this first term because 9 is a power of 3.

00:44 So we can write this as 3 squared to the x plus 2.

00:51 And the reason why we want to do that is that if they have the same base, we can go a lot further with operations on these terms.

01:00 And so we can also simplify this again to 3.

01:04 To the 2 parentheses x plus 2 using our exponent rules.

01:14 So now that they have the same base, let's go ahead and add this second term over to the other side.

01:20 So we get 3 to the 2 parentheses x plus 2 power equals 3 to the x squared plus 2x power.

01:31 Since they have the same base, we can really simply bring down the exponents.

01:36 We just have to log base 3 both sides.

01:38 So if we do that, we get the exponents are equaling each other.

01:42 We get two, parentheses, x plus two, equals x squared plus 2x.

01:51 And now this is just a quadratic.

01:54 So let's go ahead and distribute this expression...

Question

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