Where do the graphs of x+y=65 and x^2+y^2=194 cross (if they cross)?
1 Answer | Add Yours
We have the equations
1) `x + y = 65`
2) `x^2 + y^2 = 194`
Solve the first equation for y:
`y = 65 - x`
Substituting into the second equation we obtain
`x^2 + (65-x)^2 = 194`
` `which implies that
`x^2 + 65^2 - 2(65)x + x^2 - 194 = 0`
`implies` `2x^2 -130x + 4031 = 0`
Using the quadratic formula we find that
`x = (130 pm sqrt(130^2 - 4(2)(4031)))/4 = 130/4 pm sqrt(-15348)/4`
Therefore there is no Real solution for `x`.
To check this look at the plotted graphs
The graphs - a line y = 65 - x and a circle, center (0,0) radius sqrt(194) -
don't cross. Therefore the system of equations has no Real solutions.
The complex (conjugate) solutions satisfy
x = 130/4 +/- sqrt(-15348)/4
Join to answer this question
Join a community of thousands of dedicated teachers and students.Join eNotes