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# Nonlinear Systems of Equations

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## Nonlinear Systems of Equations Answer Key

1.
At what point(s) do the equations $y=x^2+4x+4$ and $y=12x+24$ 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 $y=x^2+2x+4$ and $y=-x^2+2x+6$ 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?
$y=2x+6$
$x^2+(y+4)^2=10$
1. $(0,6)$
2. No intersection
3. $(1+sqrt(5), 4+2sqrt(5)), \ (1-sqrt(5), 4-2sqrt(5))$
4. $(4,-2), \ (9,-12)$

4.
Find the point(s) of intersection of the following equations.
$y=4x+2$
$y=2(x-1)^2-2$
1. No intersection
2. $(1,6), \ (-1,-2)$
3. $(2+sqrt(3),10+4sqrt(3)), \ (2-sqrt(3), 10-4sqrt(3))$
4. $(2+sqrt(5),10+4sqrt(5)), \ (2-sqrt(5),10-4sqrt(5))$
5.
Find the solution(s).
$y=-2x+2$
$y=-x^2+5$
• (3 , -4)
(-1 , 4)

6.
Solve the system of equations.
$(x-2)^2+(y-3)^2=16$
$y=3x+1$
• $(-2/5, -1/5)$
$(2, 7)$
7.
Solve the system of equations.
$y=3x^2+5x-2$
$y=17x-14$
• (2, 20)

8.
Find the solution(s).
$y=.5x^2 -6$
$y=3x+2$
• (-2 , -4)
(8 , 26)
9.
Solve the system of equations.
$y = 5x^2-6$
$y=4x^2+x$
• (-2, 14)
(3, 39)

10.
Solve the system of equations.
$(x-1)^2+(y+2)^2=25$
$y=4/3x+5$
• (-3, 1)
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