SOLUTION: sketch each system of equations. Then solve the system by the substitution method x^2 + y^2=6 y=x^2

Question 1088793: sketch each system of equations. Then solve the system by the substitution method
x^2 + y^2=6
y=x^2
Answer by ikleyn(52902) (Show Source): You can put this solution on YOUR website!
.
sketch each system of equations. Then solve the system by the substitution method
x^2 + y^2=6
y=x^2
~~~~~~~~~~~~~~~~~~

 = 6,     (1)
y = .        (2)





Plots  = 6   and  y = .



To solve the system, replace  in the equation (1) by y, according to (1). You will get

y + y^2 = 6,         (3)   or

 = 0,         (4)

(y+3)*(y-2) = 0  ====>  the roots are  = -3  and   = 2.


Since y = ,  y must be positive, so only the root y = 2 survives.


Then x = +/- .


Answer. The solutions to the system  (1),(2)  are  (x,y) = (,)  and  (x,y) = (,).

To see more solved samples of such systems, look into the lesson
- Solving the system of algebraic equations of degree 2
in this site.

Also, you have this free of charge online textbook in ALGEBRA-I in this site
- ALGEBRA-I - YOUR ONLINE TEXTBOOK.

The referred lesson is the part of this online textbook under the topic "Systems of equations that are not linear".

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