Nonlinear Systems

Question 1

Solve the system x^2 + y^2 = 169 and y = x - 7. Give the solutions as ordered pairs.

Accepted Answer

(12, 5) and (-5, -12)

Answer

(5, 12) and (-12, -5)

Answer

(12, 5) and (5, -12)

Answer

(13, 6) and (-6, -13)

Question 2

Solving x^2 + y^2 = 23 and y = x^2 - 3, a student substitutes x^2 = y + 3, gets y^2 + y - 20 = 0, finds y = 4 and y = -5, and reports four solution points. What is wrong?

Accepted Answer

y = -5 forces x^2 = -2, so it gives no real points

Answer

the substitution should have been y^2 = x + 3

Answer

the quadratic factors to give y = -4 and y = 5

Answer

nothing is wrong, because a circle and a parabola meet four times

Question 3

Solve the system x^2 + y^2 = 25 and 2x^2 - y^2 = 2 by adding the equations. Give all solutions as ordered pairs.

Accepted Answer

(3, 4), (3, -4), (-3, 4) and (-3, -4)

Answer

(4, 3), (4, -3), (-4, 3) and (-4, -3)

Answer

(9, 16), (9, -16), (-9, 16) and (-9, -16)

Answer

(5, 0), (-5, 0), (0, 4) and (0, -4)

Question 4

How many points do the circle x^2 + y^2 = 25 and the vertical line x = 6 have in common?

Accepted Answer

none

Answer

exactly one

Answer

exactly two

Question 5

Solve the system x^2 + y^2 = 169 and y = x + 7. Give the solutions as ordered pairs.

Accepted Answer

(5, 12) and (-12, -5)

Answer

(12, 5) and (-5, -12)

Answer

(5, 12) and (12, -5)

Answer

(6, 13) and (-13, -6)

Question 6

Solve the system x^2 + y^2 = 225 and 2x^2 - y^2 = 18 by adding the equations. Give all solutions as ordered pairs.

Accepted Answer

(9, 12), (9, -12), (-9, 12) and (-9, -12)

Answer

(12, 9), (12, -9), (-12, 9) and (-12, -9)

Answer

(81, 144), (81, -144), (-81, 144) and (-81, -144)

Answer

(15, 0), (-15, 0), (0, 12) and (0, -12)

Question 7

Solving x^2 + y^2 = 34 and y = x^2 - 4, a student substitutes x^2 = y + 4, gets y^2 + y - 30 = 0, finds y = 5 and y = -6, and reports four solution points. What is wrong?

Accepted Answer

y = -6 forces x^2 = -2, so it gives no real points

Answer

the substitution should have been y^2 = x + 4

Answer

the quadratic factors to give y = -5 and y = 6

Answer

nothing is wrong, because a circle and a parabola meet four times

Question 8

Solve the system x^2 + y^2 = 625 and y = x + 17. Give the solutions as ordered pairs.

Accepted Answer

(7, 24) and (-24, -7)

Answer

(24, 7) and (-7, -24)

Answer

(7, 24) and (24, -7)

Answer

(8, 25) and (-25, -8)

Question 9

How many points do the circle x^2 + y^2 = 64 and the vertical line x = -5 have in common?

Accepted Answer

exactly two

Answer

none

Answer

exactly one

Question 10

Solve the system x^2 + y^2 = 225 and y = x + 3. Give the solutions as ordered pairs.

Accepted Answer

(9, 12) and (-12, -9)

Answer

(12, 9) and (-9, -12)

Answer

(9, 12) and (12, -9)

Answer

(10, 13) and (-13, -10)

Question 11

Solve the system x^2 + y^2 = 25 and 2x^2 - y^2 = 23 by adding the equations. Give all solutions as ordered pairs.

Accepted Answer

(4, 3), (4, -3), (-4, 3) and (-4, -3)

Answer

(3, 4), (3, -4), (-3, 4) and (-3, -4)

Answer

(16, 9), (16, -9), (-16, 9) and (-16, -9)

Answer

(5, 0), (-5, 0), (0, 3) and (0, -3)

Question 12

Solve the system x^2 + y^2 = 289 and y = x - 7. Give the solutions as ordered pairs.

Accepted Answer

(15, 8) and (-8, -15)

Answer

(8, 15) and (-15, -8)

Answer

(15, 8) and (8, -15)

Answer

(16, 9) and (-9, -16)

Question 13

Solve the system x^2 + y^2 = 100 and y = x + 2. Give the solutions as ordered pairs.

Accepted Answer

(6, 8) and (-8, -6)

Answer

(8, 6) and (-6, -8)

Answer

(6, 8) and (8, -6)

Answer

(7, 9) and (-9, -7)

Question 14

Solve the system x^2 + y^2 = 100 and 2x^2 - y^2 = 8 by adding the equations. Give all solutions as ordered pairs.

Accepted Answer

(6, 8), (6, -8), (-6, 8) and (-6, -8)

Answer

(8, 6), (8, -6), (-8, 6) and (-8, -6)

Answer

(36, 64), (36, -64), (-36, 64) and (-36, -64)

Answer

(10, 0), (-10, 0), (0, 8) and (0, -8)

Question 15

Solving x^2 + y^2 = 14 and y = x^2 - 2, a student substitutes x^2 = y + 2, gets y^2 + y - 12 = 0, finds y = 3 and y = -4, and reports four solution points. What is wrong?

Accepted Answer

y = -4 forces x^2 = -2, so it gives no real points

Answer

the substitution should have been y^2 = x + 2

Answer

the quadratic factors to give y = -3 and y = 4

Answer

nothing is wrong, because a circle and a parabola meet four times

Question 16

How many points do the circle x^2 + y^2 = 36 and the line y = 7 have in common?

Accepted Answer

none

Answer

exactly one

Answer

exactly two

Question 17

Solving x^2 + y^2 = 21 and y = x^2 - 1, a student substitutes x^2 = y + 1, gets y^2 + y - 20 = 0, finds y = 4 and y = -5, and reports four solution points. What is wrong?

Accepted Answer

y = -5 forces x^2 = -4, so it gives no real points

Answer

the substitution should have been y^2 = x + 1

Answer

the quadratic factors to give y = -4 and y = 5

Answer

nothing is wrong, because a circle and a parabola meet four times

Question 18

Solve the system x^2 + y^2 = 289 and 2x^2 - y^2 = -97 by adding the equations. Give all solutions as ordered pairs.

Accepted Answer

(8, 15), (8, -15), (-8, 15) and (-8, -15)

Answer

(15, 8), (15, -8), (-15, 8) and (-15, -8)

Answer

(64, 225), (64, -225), (-64, 225) and (-64, -225)

Answer

(17, 0), (-17, 0), (0, 15) and (0, -15)

Question 19

How many points do the circle x^2 + y^2 = 25 and the line y = -8 have in common?

Accepted Answer

none

Answer

exactly one

Answer

exactly two

Question 20

How many points do the circle x^2 + y^2 = 9 and the vertical line x = 7 have in common?

Accepted Answer

none

Answer

exactly one

Answer

exactly two

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Nonlinear Systems

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Nonlinear Systems

Ways to Play

Device Games: Students play on their phones

Blast Go

Zombie Escape

Avalanche

Maze Blast

Cave Climb

Blast Out

Mystery Auction

Tour Guide

Food Truck Rush

Tug of War

Alien Blast

Glacier Rush

Board Games: Teacher-led, projected to the class

Like what you see?

More like this

Bug Blast

BlastRace

BlastQuiz

BlastBoard

Seek & Destroy

Mystery Blast

Checkers

Texas Hold 'Em

Da Bomb

Castle Siege

Hot Potato

Market Mayhem

King of the Hill

Bank Heist

Top Corner