5

Points) Find the general solution to the system of equations 60x 22y + 9e165x 61y.Both of your functions must be correct to receive creditx(t)y(t)...

Question

Points) Find the general solution to the system of equations 60x 22y + 9e165x 61y.Both of your functions must be correct to receive creditx(t)y(t)

points) Find the general solution to the system of equations 60x 22y + 9e 165x 61y. Both of your functions must be correct to receive credit x(t) y(t)



Answers

Concept Check A nonlinear system is given, along with the graphs of both equations in the system. Verify that the points of intersection specified on the graph are solutions of the system by substituting directly into both equations.
$x+y=-3$ $x^{2}+y^{2}=45$

This problem we are asked to verify whether non negative 63 and three negative six are the solutions for this system of equations. So in the book they graft the system of equations to obtain this solution. So what we have to do is we have to prove or verify that is true. So all you have to do is plug each solution into the system and see if it's true. So I'm gonna go ahead and prove my first solution negative 63 were negative six. Is your ex value to use your wife value. So for the first equation is going to become negative six Plus Why? Which will be 3? And does that equal to -3? And negative six plus three m in the equal to negative three. So that's true. And now you're gonna do something with the second equation X squared is going to become negative six square plus wide square y. It's gonna is three. So it's gonna be three squared. And does that equal to 45? So again um any number square is always positive. So negative six squares 36 positive 36 plus three square is nine and 36 plus nine does in the equals 45. So therefore we have verified that -63 is one of the solutions. So now we need to verify that 363 negative six is the other solution. So you do the same thing, you're going to plug into your equations. So in the first equation is going to become three plus Why? Which is negative? six Equals 2 -3. Three plus negative six is same thing as three minus six equals negative three. And three minus six does equal to negative. So that's true. And now you do the same thing with the second equation, plug in. So x square will be three square. Yeah Plus Why Square Why will be -6? And does that equal to 45? So three square is nine? Any number score is positive, so negative six score is 36 And nine plus 36 does equal to 45. So therefore we have verified again to show that 3 -6 Is our 2nd solution.

This question we're asked to verify that the points of intersection from the graph are the solutions for this system of nonlinear equations. So to do that, all you have to do is directly substitute those points into your equation. So the first point that I'm going to check is negative two negative one. Where negative two is your ex value and negative one is your wife value. And you're gonna plug that into the equation one. And the equation to. So in equation one x square is going to become negative two square plus. Why school is going to become negative one square and that's going to give you five. Is that true? Let's see negative two square is going is positive for because negative two squared means negative two times negative two negative negative becomes positive. Or you you should also remember any number squared is always positive so therefore negative one square is also positive one and four plus one does equal to five. So that's true. And now I'm going to do the same thing, plug plus negative two negative one into my second equation. So this is going to become negative three times negative two plus four times the y value is negative one equals to chew negative three times negative two. That's positive six. Four times negative one is negative four. So it's gonna be minus four and six minus four does indeed equal to two. So that's true. So the second solution I'm going to check is 38/25 and 41 over 25. So again where the first number is your ex value. Second number is your wife value and you're going to do the same thing. Put that solution into each equation. So my first equation is going to become X squared is going to be 38/25 squared plus. Why is 41 over 25 squared? And does that equal to five? Okay, So you might have to use your calculator to square this fraction. So when I use calculator, the first fraction is going to become 1444 over 6. 25 plus. Okay, 1681 over 6. 25. And does that give you five? So because they have the same denominator, I can just add the numerous together, which gives me 3125 over 6. 25. And if you take out your calculator it does indeed equals 25 So it's correct for the first equation and now you're going to do again for the second equation. So your second equation is gonna become negative three times X is 38/25 plus four times. Why? Why is 41/25? And does our final answer equals to two? Okay, so again you can use your calculator to help you both by negative three times 38/25 which gives you negative 114 over 25 plus four times 41 is 1 64/25 equals to two. And again they have the same denominator. So I can just add a numerous together negative 1 14 plus 1 60 for that gives you 50 and then bring down the common denominator and 50. The value of 25 does E. D. Equal to two. So therefore the solutions hey from the graph are correct.

For this question, we're asked to verify whether or not the solutions to this system of equations are 38/25, 41/25 And negative, 2 -1. Those solutions were obtained from graphing and now we need to prove if it's actually true Algebraic Lee. So what you have to do is you can directly substitute these solutions into your system and see if it's equal to each other. So let's verify our first solution. 30/25 and 41/25 where this is your X value and this is your wife value. So let's go ahead and plug into our first equation. So x square is going to be 38/25 squared Plus. Why is 41/25 squared And that and those are equal to five. So you can use your calculator to help you square the fraction. So 38 square is 1000 444, 25 square is six, Plus. sq is 1,681. And then 25 Squares, six, And does that equal to five? So because they have the same denominator, I can add these two fractions. So my common denominator is 625 and then I can just add numerator. When I add those two numbers together, I get 3000 125. And if you put this in the calculator, 3,125 divided by 6:25, it does indeed equals 25. And now I'm going to do the same thing. Put this solution into my second equation. So this will become negative three times X. Which is 38/25 Plus four times wide, which is 41/25. And does that equal to chill? So again, you can use your capital to help you multiply by fraction but negative three times 38 gives you negative 114 over 25 Plus four times 41 is 160 for over 25 Equals to two. And again I have the same denominators so I can combine the fractions with common denominator of 25 and add the numerator is together. That gives me 50 And 50. The Bible 25 does indeed equals to two. So therefore we have verified that one of the solutions for this system of equations. Is this? So now let's verify the second solution negative to negative one where x is negative two and why is negative one? And you're gonna do the same thing, plug into your equation. So x squared plus y squared is going to become negative two squared Plus -1 square. Yeah. And does that equal to five? Let's see negative two square. Any number score is always positive. So this is positive four plus negative one. Score is positive one and four plus one does indeed equals 25 And now let's check out. Second equation negative three times X X is negative two. Yeah. Plus four times white. Why is negative one? And as I equal to two. So negative three times negative two. That's going to be positive six. Four times negative one. That's gonna be negative for. So it's gonna be minus four and six months. Four doesn t equals to two. So therefore we have verified that our second solution is negative two negative one.

Can be a system X plus Y equals negative three and expert plus Y squared equals 45. From the graphs we can see that there are intersections that negative 63 and three negative six. To verify them, we substitute negative six for X and three for wine to both equations to verify negative six plus three is equal to negative three. That is true. Negative six squared plus three squared. That's 36 plus nine. That's 45. That checks out. So negative +63 is definitely a solution. Three, negative six would be three plus negative six equals negative three and that is true. And the second one will be three squared plus negative six squared equals 45. Well, that's nine plus 36 which is 45. Okay.


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