BIM ALGII 3.5 Solving Systems of Non-Linear Eq

BIM ALGII 3.5 Solving Systems of Non-Linear Eq

Why can't atheists solve exponential equations?

Because they don't believe in higher powers.

Parabola and Line Intersections:

1) 2 intersections-2 solutions

2) 1 intersections-1 solutions

3) 0 intersections-no solutions.

Types of Parabola and Line Intersections:

1) 2 intersections-2 solutions

 $y=x^2-2$  and  $y=2x+1$  

 $x^2-2=2x+1$  

 $x^2-2x-2-1$   

 $x^2-2x-2-1=0$   
 $x^2-2x-3=0$  
 $\left(x-3\right)\left(x+1\right)=0$  
 $x=3\ and\ x=-1$  

 
 $x=3\ and\ x=-1$  
Plug into one of the equations
y=2(3)+1=7    (3,7)
y=2(-1)+1=-1  (-1,-1)

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Types of Parabola and Line Intersections:

2) 1 intersections-1 solutions

 $y=x^2-6x+3\ \&\ y=2x-13$  

 $x^2-6x+3=2x-13$   
 $x^2-6x-2x+3+13=0$  
 $x^2-8x+16=0$  

 $x^2-8x+16=0$  
 $\left(x-4\right)^2=0$  
 $x=4$      $y=2\left(4\right)-13$  
 $y=-5$   Solution (4,-5)

Types of Parabola and Line Intersections:

3) 0 intersections-No real solutions, only imaginary solutions.

 $y=x^2-1\ \ \&\ y=2x-3$  

 $x^2-1=2x-3$  
 $x^2-2x-1+3=0$  
 $x^2-2x+1=-2+1$  
 $\left(x-1\right)^2=-1$  
 $\sqrt{\left(x-1\right)^2\ }$  = $\sqrt{-1}$  
No Real Solutions

Parabola intersection Parabola

1) 2 intersections

2) 1 intersections

3) No intersections

 $y=x^2-4x+1$  &  $y=-x^2+6x-7$  +(-1)  $\left(y=-x^2+6x-7\right)$  

 $y=x^2-4x+1$  
 $-y=x^2-6x+7$  
 $0=2x^2-10x+8$  

 

 $0=2x^2-10x+8$  
 $x^2-5x+4=0$  
(x-4)(x-1)=0
x=4 and x=1
4*4-4(4)+1=1  (4,1)
1*1-4*1+1=-2  (1,-2)
2 solutions

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Circle and Line.

1) 2 intersections

2) 1 intersections

3) No intersections

Solve the two equations for the intersections on your white board tables.
y=3x-5

 $x^2+y^2=5$  

 $x^2+\left(3x-5\right)^2=5$   $x^2+9x^2-30x+25=5$   $10x^2-30x+20=0$   $\ \ \ \ x^2-3x+2=0$  $\ \ \ \ \ \left(x-2\right)\left(x-1\right)=0$  

x=2 and x=1

x=2 so y=3(2)-5

y=1 so sol(2,1)

x=1 so y=3(1)-5

y=-2 so (1,-2)

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I'd have *n* dollars

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