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Systems - Calculus - Exercise, Exercises of Calculus

National Institute of Industrial EngineeringCalculus

This file contains some problems related calculus. Some hints to the given problems are: Systems, Equations, System by Substitution, No Solution, System Algebraically, System by Elimination, Answer Key

Typology: Exercises

2011/2012

Uploaded on 12/31/2012

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aparijita 🇮🇳

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bg1
Systems of Equations
Solvethesystembysubstitution.
1) x+y=10
x-y=8
A) Nosolution B) (8
,
2) C) (9
,
1) D) (-9
,
2)
2) x+6y=0
x-6y=36
A) (18
,
-3) B) (-3
,
18) C) (18
,
3) D) (6
,
-1)
3) x+2y=14
-2x+3y=21
A) (1
,
6) B) Nosolution C) (-7
,
0) D) (0
,
7)
4) x-y2=0
x-16=0
A) (16
,
±4) B) (16
,
±16) C) (±4
,
16) D) (16
,
4)
5) y-x2=3x
y=x-1
A) (-1,-4)and(-1
,
-2) B) (-1,-2)and(-1
,
-2)
C) (-1,-2) D) (-1,-2)and(-1
,
-3)
Solvethesystemalgebraically.
6) y=x3+x2
y=3x2
A) (2
,
12) B) (0,0)and(2
,
12) C) (0,0)and(4
,
48) D) (0,0)and(2
,
8)
7) y=x3-x2
y=3x2
A) (0,0)and(2
,
12) B) (4
,
48) C) (0,0)and(4
,
48) D) (0,0)and(4
,
64)
8) y=20x2
7x+y=3
A) 1
4,5
4and3
5,36
5B) 1
4,5
4and-3
5,36
5
C) -1
4,5
4and3
5,36
5D) -1
4,5
4and-3
5,36
5
9) y=25x2+x
9x+y=3
A) 1
5,6
5and3
5,48
5B) -1
5,4
5and3
5,48
5
C) -1
5,4
5and-3
5,42
5D) 1
5,6
5and-3
5,42
5
pf3

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Systems of Equations

Solve the system by substitution.

  1. x + y = 10 x - y = 8 A) No solution B) (8, 2) C) (9, 1) D) (-9, 2)

  2. x + 6y = 0 x - 6y = 36 A) (18, - 3) B) (-3, 18) C) (18, 3) D) (6, - 1)

  3. x + 2y = 14

  • 2x + 3y = 21 A) (1, 6) B) No solution C) (-7, 0) D) (0, 7)

  1. x - y2^ = 0 x - 16 = 0 A) (16, ±4) B) (16, ±16) C) (±4, 16) D) (16, 4)

  2. y - x2^ = 3x y = x - 1 A) (-1, - 4) and (-1, - 2) B) (-1, - 2) and (-1, - 2) C) (-1, - 2) D) (-1, - 2) and (-1, - 3)

Solve the system algebraically.

  1. y = x3^ + x y = 3x A) (2, 12) B) (0, 0) and (2, 12) C) (0, 0) and (4, 48) D) (0, 0) and (2, 8)

  2. y = x3^ - x y = 3x A) (0, 0) and (2, 12) B) (4, 48) C) (0, 0) and (4, 48) D) (0, 0) and (4, 64)

  3. y = 20x 7x + y = 3 A) 1 4

and 3 5

B) 1

and - 3 5

C) - 14 , 54 and 35 , 365 D) - 14 , 54 and - 35 , (^365)

  1. y = 25 x2^ + x 9x + y = 3 A) 15 , 65 and 35 , 485 B) - 15 , 45 and 35 , (^485)

C) - 1

and - 3 5

D) 1

and - 3 5

PreCalculus

  1. x2^ + y2^ = 4 x + 2y = 3

A) 3 -^2 5

, 6 +^11

and 3 +^2 5

, 6 -^11

B) 3 -^4

, 6 +^2

and 3 +^4 5

, 6 -^2

C) 3 -^2

, 6 -^11

and 3 +^2 5

, 6 +^11

D) 9 -^2

, 6 +^2

and 9 +^2 5

, 6 -^2

  1. x2^ + y2^ = 12 3x - y = - 2

A) -^3 +^29 5

, -^7 +^3

and -^3 -^29 5

, -^7 -^3

B) -^3 +^2

, 1 +^3

and -^3 -^6 5

, 1 -^6

C) -^3 +^29

, 1 -^3

and -^3 -^29 5

, 1 +^3

D) -^3 +^29

, 1 +^3

and -^3 -^29 5

, 1 -^3

Solve the system by elimination.

    • 7x + 8y = - 16
  • 4x + 6y = - 12 A) (0, - 2) B) (0, - 1) C) (-1, - 1) D) No solution
    • 7x + 7y = 28
  • 2x - 3y = 8 A) (-5, 1) B) (-4, 0) C) No solution D) (-4, 1)

  1. 7x + 37 = 8y 5x - 2y = 7 A) (5, 10) B) No solution C) (4, 10) D) (5, 9)

    • 5x + 7y = - 50
  • 10x = - 52 - 14y A) (3, - 5) B) (3, 8) C) No solution D) (6, 8)

  1. 5x - 8y = - 20 2x + 7y = 43 A) (-4, 5) B) (4, 5) C) No solution D) (-8, - 3)

  2. 4x + 9y = 99

  • 2x - 5y = - 53 A) No solution B) (9, 8) C) (9, 7) D) (8, 8)

Calin M. Agut - 2012