- #1
aricho
- 71
- 0
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
x+y=8
x^2-y^2=36
find the values for x and y
Thanks
Yup. This is correct. Since you have 2 unknowns, you need 2 equations. And you have already had 2 equations. You can then solve: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?
HallsofIvy said:Your statement is correct but is not a solution to the "problem" which, I suppose, was to solve the two 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.
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.
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).
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.
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.