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Systems Two by Two - Calculus - Exercise, Exercises of Calculus

Aligarh Muslim UniversityCalculus

These are the notes of Exercise of Calculus. Key important points are: Systems, Equations, System by Substitution, No Solution, System Algebraically, System by Elimination, Answer Key

Typology: Exercises

2012/2013

Uploaded on 02/11/2013

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Linear Systems 2 by 2
Findthevalueofthedeterminant.
1)
49
75
A) -43 B) 83 C) 43 D) 1
2)
-1-5
-8-9
A) -31 B) 49 C) 31 D) -67
3)
22
-11
A) 4 B) 0 C) -4D)5
4)
12 -7
-43
A) 8 B) 64 C) -8D)4
SolvethesystemofequationsusingCramerʹsRuleifitisapplicable.IfCramerʹsRuleisnotapplicable,sayso.
5)
6x+5y=-
14
4x+y=-
14
A) x=-4
,
y=2;(-4
,
2) B) x=2
,
y= -4;(2
,
-4)
C) x=-2
,
y=-4;(-2
,
-4) D) x=4
,
y= -2;(4
,
-2)
6)
4x+5y=35
4x+4y=32
A) x=5
,
y=3;(5
,
3) B) x=3
,
y=5;(3
,
5)
C) x=-3
,
y=5;(-3
,
5) D) x= -5
,
y= -3;(-5
,
-3)
7)
2x+3y=13
3x-3y=-
3
A) x=2
,
y=3;(2
,
3) B) x=3
,
y=2;(3
,
2)
C) x=-3
,
y=2;(-3
,
2) D) x= -2
,
y= -3;(-2
,
-3)
8)
5x-5y=2
25x-25y=6
A) x=5
,
y=3;(5
,
3) B) x=4
15 ,y=-4
15 ;4
15 ,-4
15
C) x=2
,
y=6;(2
,
6) D) notapplicable
pf3

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Linear Systems 2 by 2

Find the value of the determinant.

4 9 7 5 A) - 43 B) 83 C) 43 D) 1

A) - 31 B) 49 C) 31 D) - 67

A) 4 B) 0 C) - 4 D) 5

A) 8 B) 64 C) - 8 D) 4

Solve the system of equations using Cramerʹs Rule if it is applicable. If Cramerʹs Rule is not applicable, say so.

6x + 5y = - 14 4x + y = - 14 A) x = - 4, y = 2; (-4, 2) B) x = 2, y = -4; (2, - 4) C) x = - 2, y = - 4; (-2, - 4) D) x = 4, y = -2; (4, - 2)

4x + 5y = 35 4x + 4y = 32 A) x = 5, y = 3; (5, 3) B) x = 3, y = 5; (3, 5) C) x = - 3, y = 5; (-3, 5) D) x = -5, y = -3; (-5, - 3)

2x + 3y = 13 3x - 3y = - 3 A) x = 2, y = 3; (2, 3) B) x = 3, y = 2; (3, 2) C) x = - 3, y = 2; (-3, 2) D) x = -2, y = -3; (-2, - 3)

5x - 5y = 2 25x - 25y = 6 A) x = 5, y = 3; (5, 3) B) x = 4 15

, y = - 4 15

C) x = 2, y = 6; (2, 6) D) not applicable

PreCalculus

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)

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