Solve the system x+y=9, x^2 - y^2 = 36 for x and y

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In summary, the conversation was about solving a pair of equations with two unknowns. The equations given were x+y=8 and x^2-y^2=36. One person provided a solution of x=6.25 and y=1.75, while another person pointed out that the statement was correct but not a solution to the problem. Eventually, it was agreed that two equations were needed to solve for x and y.
  • #1
aricho
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Hi, i just sat my maths exam, and i had a very strange question... i don't know how to do it...

x+y=8
x^2-y^2=36

find the values for x and y

Thanks
 
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  • #2
y = 8-x

x^2 - (8-x)^2 = 36

x^2 - (64-16x+x^2) = 36

16x - 64 = 36
 
  • #3
is that it?

i did y^2-x^2=36
(x-y)(x+y)=36
(x-y)(8)=36
x-y=36/8

is any of that correct?
 
  • #4
According to Whozum, 16x- 64= 36 so x= 100/16= 25/4= 6.25 and y= 8- 6.25= 1.75.

x-y= 6.25- 1.75= 4.5 and 36/8= 9/2= 4.5.

Your statement is correct but is not a solution to the "problem" which, I suppose, was to solve the two equations.

In fact, the only thing strange I see about your "question" is that there was no "question"! Are you sure you didn't leave something out- like "solve this pair of equations" or "what are x and y"?
 
  • #5
aricho said:
is that it?

i did y^2-x^2=36
(x-y)(x+y)=36
(x-y)(8)=36
x-y=36/8

is any of that correct?
Yup. This is correct. Since you have 2 unknowns, you need 2 equations. And you have already had 2 equations. You can then solve:
[tex]\left\{ \begin{array}{l}x + y = 8 \\ x - y = \frac{9}{2} \end{array} \right.[/tex]
for x, and y.
Viet Dao,
 
  • #6
HallsofIvy said:
Your statement is correct but is not a solution to the "problem" which, I suppose, was to solve the two equations.

Me or him?
 

1. What is a system of equations?

A system of equations is a set of two or more equations that have multiple variables. The goal is to find values for each variable that satisfy all of the equations in the system.

2. How can I solve a system of equations?

There are various methods for solving a system of equations, such as substitution, elimination, and graphing. In this particular system, we can use substitution by solving for one variable in one equation and substituting it into the other equation.

3. What is the solution to the given system of equations?

The solution to this system is x=4 and y=5. When we substitute x=4 into the second equation, we get (4)^2 - y^2 = 36, which simplifies to 16 - y^2 = 36. Solving for y, we get y=5. Therefore, the solution is (4,5).

4. Can this system have multiple solutions?

No, this system can only have one solution. Since there are two equations and two variables, there is only one point where they intersect and satisfy both equations at the same time.

5. How can I check if my solution is correct?

You can check your solution by plugging in the values for x and y into the original equations and seeing if they hold true. For example, when we substitute x=4 and y=5 into the first equation, we get 4+5=9, which is true. Similarly, when we substitute these values into the second equation, we get (4)^2 - (5)^2 = 36, which is also true. Therefore, our solution is correct.

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