Grade 10 - Linear-Equations-in-Two-Variables

(Sample Online worksheet)

Choose correct answer(s) from given choice

1)The father's age is 7 times his daughter's age. After 12 years, the age of the father will be 17/5 times his daughter's age. The present ages of the daughter and the father are, respectively
a. 8 years and 56 years b. 9 years and 63 years
c. 10 years and 70 years d. 7 years and 49 years
2)The pair of equations 2x - y - 2 = 0 and -6x + 7y + 5 = 0 have
a. a unique solution b. exactly two solutions
c. infinitely many solutions d. no solution
3)Find value of k such that equations 6x + ky + 4 = 0 and 3x - 3y + 2 = 0, represents coincident lines.
a. -6 b. -7
c. 6 d. -5
4)For which value of m, following pair of linear equations have no solution.
m x + 16 y = m
4 x + m y = m - 4
a. -4 b. 4
c. -8 d. 8
5)The pair of equations y = 3 and y = -8 has
a. no solution b. two solutions
c. infinitely mainy solution d. an unique solution
6)A two digit number is 3 more than 4 times the sum of its digits. If 27 is added to the number, the digit interchange their places. Find the number.
a. 38 b. 74
c. 47 d. 56
7)For which value of λ, following pair of linear equations have infinitely many solutions.
λ x + y = λ2 and x + λ y = 1
a. 1 b. 0
c. 2 d. -1
8)Which of the following conditions is true if the system of equations below is shown to be inconsistent
a1x + b1y + c1 = 0, a2x + b2y + c2 = 0
a.  
a1
a2
  =  
b1
b2
  =  
c1
c2
 
b.  
a1
a2
  ≠  
b1
b2
  ≠  
c1
c2
 
c.  
a1
a2
  =  
b1
b2
  ≠  
c1
c2
 
d.  
a1
b1
  =  
a2
b2
  =  
c1
c2
 
9)In a two digit number, sum of its digits is 12. If 36 is added to the number, the digit interchange their places. Find the number.
a. 57 b. 84
c. 48 d. 39
10)If thrice the daughter's age in years is added to mother's age, the sum is 59. If thrice the mother's age is added to the daughter's age, the sum is 113. Find the age of mother and daughter.
a. 35 and 8 years b. 35 and 7 years
c. 35 and 9 years d. 36 and 8 years
11)Which of the following equations has a unique solution?
a. 3x + 4y + 5 = 0, 9x + 12y + 15 = 0 b. 3x + 4y + 5 = 0, 12x + 16y + 16 = 0
c. 3x + 4y + 17 = 0, 9x + 5y + 12 = 0 d. 3x + 4y + 5 = 0, 9x + 12y + 17 = 0
12)The pair of equations x = -8 and y = 6 graphically represents lines which are
a. intersecting at (-8, 6) b. coincident
c. intersecting at (6, -8) d. parallel
13)Steven is 6 years older than his friend Mark. Steven's mother is twice as old as Steven and Mark is twice as old has his brother. The age of Steven's mother is 36 years more than the age of Mark's brother. Find the ages of Steven and Mark.
a. 30 and 36 years b. 26 and 32 years
c. 24 and 30 years d. 28 and 34 years
14)In a two digit number,its unit's digit is 2 more than ten's digit. If sum of this number and the number obtained by reversing the order of its digits is 132, find the number.
a. 46 b. 75
c. 68 d. 57
15)Robert has only $1 and $20 notes with him. If the total number of notes that he has is 21 and the amount of money with him is $ 230, then the number of $1 and $20 notes are, respectively
a. 12 and 9 b. 9 and 12
c. 8 and 13 d. 10 and 11
16)In a two digit number, the ten's digit is twice the units's digit. If 36 is added to the number, the digit interchange their places. Find the number.
a. 84 b. 63
c. 48 d. 36
17)8 pens and 7 pencils cost $97 and 6 pens and 9 pencils cost $99. Find the cost of one pen and one pencil separately.
a. $7 and $6 b. $6 and $8
c. $6 and $6 d. $6 and $7
18)7 pens and 4 pencils cost $47 and 3 pens and 4 pencils cost $27. Find the cost of 3 pens and 3 pencils.
a. $27 b. $19
c. $21 d. $24
19)There are two numbers. If three times the larger of two numbers is divided by the smaller one, we get 8 as quotient and 7 as remainder. If five times the smaller of two numbers is divided by the larger one, we get 1 as quotient and 21 as remainder. Find the numbers.
a. 28 and 11 b. 9 and 11
c. 29 and 10 d. 30 and 9
20)Michelle and Michael have some bananas. Michelle says to Michael, "ff you give me 9 of your bananas, I will have twice the number of bananas left with you". Michael replies, "if you give me 9 of your bananas I will have the same number of bananas left with you". Find the the number of bananas with Michelle and Donna separately.
a. 61 and 47 b. 61 and 43
c. 65 and 43 d. 63 and 45
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