Nonlinear Systems of Equations (Grades 11-12)

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Nonlinear Systems of Equations

1. 
At what point(s) do the equations [math]y=x^2+4x+4[/math] and [math]y=12x+24[/math] intersect?
  1. (-2, 0), (10, 144)
  2. (4, 4), (12, 24)
  3. No Intersection
  4. (3, 6), (6, 3)
 
2. 
At what point(s) do the equations [math]y=x^2+2x+4[/math] and [math]y=-x^2+2x+6[/math] intersect?
  1. No Intersection
  2. (4, 2), (6, 2)
  3. (1, 7), (-1, 3)
  4. (2, 4), (2, 6)
3. 
At what point(s) do the following equations intersect?
[math]y=2x+6[/math]
[math]x^2+(y+4)^2=10[/math]
  1. [math](0,6)[/math]
  2. No intersection
  3. [math](1+sqrt(5), 4+2sqrt(5)), \ (1-sqrt(5), 4-2sqrt(5))[/math]
  4. [math](4,-2), \ (9,-12)[/math]
 
4. 
Find the point(s) of intersection of the following equations.
[math]y=4x+2[/math]
[math]y=2(x-1)^2-2[/math]
  1. No intersection
  2. [math](1,6), \ (-1,-2)[/math]
  3. [math](2+sqrt(3),10+4sqrt(3)), \ (2-sqrt(3), 10-4sqrt(3))[/math]
  4. [math](2+sqrt(5),10+4sqrt(5)), \ (2-sqrt(5),10-4sqrt(5))[/math]
5. 
Find the solution(s).
[math]y=-2x+2[/math]
[math]y=-x^2+5[/math]






 
6. 
Solve the system of equations.
[math](x-2)^2+(y-3)^2=16[/math]
[math] y=3x+1[/math]






7. 
Solve the system of equations.
[math]y=3x^2+5x-2[/math]
[math]y=17x-14[/math]






 
8. 
Find the solution(s).
[math]y=.5x^2 -6[/math]
[math]y=3x+2[/math]






9. 
Solve the system of equations.
[math]y = 5x^2-6[/math]
[math]y=4x^2+x[/math]






 
10. 
Solve the system of equations.
[math](x-1)^2+(y+2)^2=25[/math]
[math]y=4/3x+5[/math]






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