Question 924357: {2x+y=5
{x^2+y2=50
Solve the nonlinear system by substitution
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! solve for y in the first equation to get y = 5 - 2x
replace y in the second equation with 5 - 2x to get:
x^2 + (5-2x)^2 = 50
simplify to get:
x^2 + 25 - 20x + 4x^2 = 50
combine like terms and reorder the terms to get:
5x^2 - 20x + 25 = 50
subtract 50 from both sides of the equation to get:
5x^2 - 20x - 25 = 0
factor to get:
(5x+5) * (x-5) = 0
solve for x to get:
x = -1 and x = 5
in either equation, solve for y to get:
when x = -1, y = 7
when x = 5, y = -5
when you solve for y in the first equation, you will get an ambiguous answer.
for example:
x^2 + y^2 = 50
when x = -1, you get y = plus or minus sqrt(49).
when x = 5, you get y = plus or minus sqrt(25)
y could be -7 or plus 7 when x = -1 based on the first equation.
y could be -5 or plus 5 when x = 5 based on the first equation.
however, the second equation tells you that:
when x = 5, y = 5 - 2x = 5 - 10 = -5
when x = -1, y = 5 - 2(-1) = 5 + 2 = 7
there is no ambiguity there and since the solution needs to satisfy both equations, your answer is:
(5,-5) is one of the coordinate points common to both equations.
(-1,7) is the other of the coordinate points common to both equations.
the graph of both equations is shown below:
|
|
|
