![]() ![]() Everything under the radicle is 169, which is convenientīecause that is 13 squared and so this is going to simplify. Going to be equal to four and now what do we have in here? Four times two times six is equal to 48, so this is equal to 48 and so 121 + 48 is 169, so let me write it this way. ![]() Two times a, so a is two, so two times that is Which is negative six, so I could put the six hereĪnd then make that a positive, since I'm multiplying by negative six, and then all of that over Minus the square root, 11 squared is 121, minus four times a, which is two times c, Now, this would mean that this is going to beĮqual to negative b, b is 11, so negative 11 plus or This will give us the xes thatĬan satisfy this equation. The square root of b squared minus four ac all of that over 2a. Of course tells us if this is of the form, ax squared, actually let me write it this way, if we're of the form ax squared + bx + c, we could see that two is equal to a, 11 is equal to b, and c is equal to -6 and so the quadratic formula, of course, is negative b plus or minus Is not a one over here, so the quadratic formula Not seem familiar to you, I encourage you to review that in the algebra sections of Khan Academy, but my brain goes to quadratic formula, at least for something where the leading coefficient Now to solve for x here, we might wanna factor and there's techniques for doing that or we could just go straight Now 13x - 2x is going to be 11x, so plus 11x and then we have 2 -3, so that is -6. With on the left hand side, by design, it leaves me with zero and on the right hand The 2x from both sides and I'm going to subtractĪ three from both sides and then what that leaves me That from both sides, so I'm gonna subtract The 3 on the left hand side, so I'm gonna subtract Terms onto one side, so let's get rid of the 2x and Now this looks really complex, but we're just dealing with a quadratic if we can just combine This is equal to y, so we could substitute this back in for y and we would get 2x + 3 is equal to 2x squared + 13x - 3. We just combine these two, we get it's equal to 2x + 3 and so now I can take this. To 2x plus 6 then minus 3, which is, of course, if X plus three minus three and then I could distribute out this two and so this would be equal ![]() So just focusing on this bottom equation, we can subtract three from both sides and then that would lead us to y is equal to two times Substitute back here for y and then let's let me Is on this linear one, it looks like it's solveįor y and then I could, whatever Y is equal to, I could We have a system of equationsĪnd this one looks linear. If x comma y is a solution of the system of equations aboveĪnd x is greater than zero, what is the value of xy? Pause this video and see ![]()
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