How do you solve the system #x^2+y^2=17# and #y=x+3#?
2 Answers
The Soln. Set
Explanation:
Sub.ing
These roots satisfy the eqns.
Thus, the Soln. Set
Explanation:
Here's an alternative method that tries to use symmetry to help...
Let
Then
So we have:
#17 = x^2+y^2#
#= (t-3/2)^2+(t+3/2)^2#
#= t^2-color(red)(cancel(color(black)(3t)))+9/4+t^2+color(red)(cancel(color(black)(3t)))+9/4#
#= 2t^2+9/2#
Subtract
#2t^2 = 17-9/2 = 25/2#
Divide both ends by
#t^2 = 25/4 = 5^2/2^2#
Hence:
#t = +-5/2#
If
If