SOLUTION: Help please! Solve the system of equations: a.2x+y=4 y=x^2-4x-11 b. Graph the system of equations: y=x^2-2 y=-2x+1 label the point(s) of intersection. thank you

Algebra ->  Equations -> SOLUTION: Help please! Solve the system of equations: a.2x+y=4 y=x^2-4x-11 b. Graph the system of equations: y=x^2-2 y=-2x+1 label the point(s) of intersection. thank you       Log On


   

Question 61323: Help please!
Solve the system of equations:
a.2x+y=4
y=x^2-4x-11

b. Graph the system of equations:
y=x^2-2
y=-2x+1
label the point(s) of intersection.
thank you

Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
Solve the system of equations:
a.
2x + y = 4
Rearrange in the general form (y=)
y = 4 - 2x
:
y=x^2-4x-11
Or
x^2 - 4x - 11 = y
Substitute (4-2x) for y, arranage as a quadratic eq, and solve for x:
x^2 - 4x - 11 = 4 - 2x
x^2 - 4x + 2x - 11 - 4 = 0
x^2 - 2x - 15 = 0
Factors easily to:
(x-5)(x+3) = 0
x = +5 and x = -3 are the solutions
:
Find the values of y using both solutions:
x = 5
y = 4 - 2(5)
y = 4 -10
y = -6
:
x = -3
y = 4 - 2(-3)
y = 4 - (-6)
y = 4 + 6
y = +10
:
These solutions will be apparent if we graph it:
+graph%28+300%2C+200%2C+-6%2C+6%2C+-20%2C+20%2C+x%5E2+-+4x+-+11%2C+4+-+2x%29+
:
Notice the points of intersection -3,+10 and +5,-6
:
:
:
b. Graph the system of equations:
y = x^2 - 2
y =-2x + 1
label the point(s) of intersection.
:
your graph should look like this;
+graph%28+300%2C+200%2C+-4%2C+4%2C+-4%2C+10%2C+x%5E2-2%2C-+2x%2B1+%29+
:
We can calculate the points of intersection by solving for x just like we did in the 1st problem; replace y with one of the equations:
x^2 - 2 = -2x + 1
x^2 + 2x - 2 - 1 = 0
x^2 + 2x - 3 = 0
Factors to:
(x+3)(x-1) = 0
x = -3 and x = +1 are the solutions
:
Find y using both solutions in the 2nd equation, -2x+1:
y = -2(-3) + 1
y = +6 + 1
y = +7
:
Using x = +1
y = -2(1) + 1
y = -2 + 1
y = -1
:
Our points of intersection: -3,+7 and +1,-1
:
Did this make sense to you? Any questions?