SOLUTION: Consider the following equation X^2 +y =0 y=x-2 We have two main methods to solve systems substitution and elimination. What method(s) could we use to solve this system

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Question 1044551: Consider the following equation
X^2 +y =0
y=x-2
We have two main methods to solve systems substitution and elimination. What method(s) could we use to solve this system and why?

Found 3 solutions by ikleyn, MathLover1, MathTherapy:
Answer by ikleyn(52821) About Me  (Show Source):
You can put this solution on YOUR website!
.
What do you think?
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Comment from student: substitution but not sure why?


My response. I specially took the pause to hear your answer. Thank you.

Actually both the substitution method and the elimination method lead to the same quadratic equation in just one step.


Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E2+%2By+=0....eq.1
y=x-2+......eq.2
----------------
we could use substitution to solve this system because eq2 is already solved for y

x%5E2+%2By+=0....eq.1 substitute x-2 for y
x%5E2+%2Bx-2+=0.....solve for x
x%5E2+%2Bx-2+=0..........factor completely, write x as -x%2B2x
x%5E2-x+%2B2x-2+=0...group
%28x%5E2-x%29+%2B%282x-2+%29=0
x%28x-1%29+%2B2%28x-1+%29=0
%28x%2B2%29+%28x-1%29
solutions: x=-2 or x=1
now find y
go to y=x-2+......eq.2, substitute x
y=-2-2+->y=-4
y=1-2+->y=-1

so, solutions to this system are:
x=-2 ,y=-4
or
x=1,y=-1

+graph%28+600%2C+600%2C+-10%2C+10%2C+-10%2C+10%2C+x-2%2C+-x%5E2%29+

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

Consider the following equation
X^2 +y =0
y=x-2
We have two main methods to solve systems substitution and elimination. What method(s) could we use to solve this system and why?
This is such an easy system so either can be used.

SUBSTITUTION

x%5E2+%2B+y+=+0 ------ Considering X is the same as x ------ eq (i)

y = x - 2 ------ eq (ii) 

x%5E2+%2B+x+-+2+=+0 ------ Substituting x - 2 for y in eq (i)

Solve this quadratic for x, noting that it CAN be factored.

Then substitute each value for x into any of the 2 original equations to get 2 corresponding values for y



ELIMINATION

x%5E2+%2B+y+=+0 ------ Considering X is the same as x ------ eq (i)

y = x - 2____- x + y = - 2  ------ eq (ii) 

x%5E2+%2B+x+=+2 ------- Subtracting eq (ii) from eq (i) 

x%5E2+%2B+x+-+2+=+0

Solve this quadratic for x, noting that it CAN be factored.

Then substitute each value for x into any of the 2 original equations to get 2 corresponding values for y

I guess it comes down to which method one prefers.