SOLUTION: hot to solve this system of linear/non linear equation {x^2+y=8, x-2y=-6 pls

Question 211428: hot to solve this system of linear/non linear equation

{x^2+y=8, x-2y=-6

pls
Answer by Theo(13342) (Show Source): You can put this solution on YOUR website!
x^2 + y = 8
x - 2y = -6
-----
You want to solve these simultaneously I presume.
-----
Multiply the first equation by 2 to get:
2x^2 + 2y = 16
Add the second equation of x - 2y = -6 to this to get:
2x^2 + 2y = 16
+
x - 2y = -6
=
2x^2 + x = 10 (result)(
-----
The + 2y and - 2y canceled out leaving you with one equation in one unknown which can be solved.
-----
You accomplished this by adding the left side of the equations together and the right side of the equations together separately from each other.
-----
You get 2x^2 + 2y + x - 2y on the left side of the = sign.
This becomes 2x^2 + x
-----
you get 16 - 6 on the right side of the = sign.
This becomes 10
-----
Your answer is:
2x^2 + x = 10 shown above as (result)
-----
Subtract 10 from both sides of this equation to get:
2x^2 + x - 10 = 0
Factor this equation to get:
(2x+5)*(x-2) = 0
Values for x can be:
x = 2
or:
x = -5/2
-----
Plug these values into your original equations and solve for y.
-----
First original equation is:
x^2 + y = 8
-----
Solve for y to get:
y = 8 - x^2
-----
When x = 2, y = 4
When x = -5/2, y = 1.75
-----
Second original equation is:
x - 2y = -6
Solve for y to get:
y = (x+6)/2
-----
When x = 2, y = 8/2 = 4
When x = -5/2, y = 1.75
-----
Those are your solutions:
When x = 2 and y = 4, both equations are satisfied.
When x = -5/2 and y = 1.75, both equations are satisfied.
-----
By satisfying the equations I mean that when you plug those pairs of values for x and y in both equations, they are both true.
-----
Example:
x-2y = -6
plug x = 2 and y = 4 into this equation to get:
2 - 2*(4) = -6
This becomes:
2 - 8 = -6 which becomes -6 = -6 which is true.
-----
Similarly, the equation of:
x^2 + y = 8 becomes:
2^2 + 4 = 8 which becomes:
4 + 4 = 8 which becomes 8 = 8 which is true.
-----
Likewise, take:
x-2y = -6
plug x = -5/2 and y = 1.75 into it to get:
since -5/2 = -2.5, we'll use -2.5 in place of -5/2
-----
x-2y = -6 becomes:
-2.5 - 2*(1.75) = -6 which becomes:
-2.5 - 3.5 = -6 which becomes -6 = -6 which is true.
Similarly, the equation of:
x^2 + y = 8
becomes
(-2.5)^2 + 1.75 = 8 which becomes:
6.25 + 1.75 = 8 which becomes:
8 = 8 which is true.
-----

RELATED QUESTIONS
How do I solve this non-linear system of equation? 6x^2+y^2=1... (answered by ankor@dixie-net.com)

solve the following non-linear system of equations. x^2 + 2y^2 = 3 x - y^2 =... (answered by jim_thompson5910)

Solve the non-linear system of equations. Give Exact Values: {{{x^2+y^2=25}}}... (answered by ankor@dixie-net.com)

Solve the following system of non-linear equations. y=x^2-2x-33... (answered by ikleyn)

Please help me solve this equation what is the linear system? x-2y=8... (answered by ewatrrr)

I'm sturggling with this problem. Any help would be greatly appreciated. Solve the... (answered by stanbon,checkley71)

Help On This Will Be Great Appreciated<3 Solve The Non-Linear system of Equations. Give... (answered by Earlsdon)

Solve this system of linear equations: {{{y=x-2}}}... (answered by math-vortex)

Solve the following system of linear inequalities by graphing x-y<3 x+2y>6 Please... (answered by checkley75)