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Question (1):
Which of the following equations have x=2, y=3 as solution ? (a) 8x-y = 12 (b) 2x+3y = 10 |
Answer:
(a) Substitute x=2, y=3 in 8x-y=12 8(2)-3=12 16-3=12  x=2, y=3 is not a solution of 8x-y=12 (b) Substitute x=2, y=3 in 2x+3y=10 2(2)+3(3)=10 4+9=10  x=2, y=3 is not a solution of 2x+3y=10. |
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Question (2):
Find the values of a so that x=1, y=2 is a solution of: (a) 2x+ay=10 (b) ax+2y=6 (c) x+2y=a |
Answer:
(a) 2x+ay=10, substitute x=1, y=2 2(1)+a(12) = 10 2+2a=10 2a=8 a=4 (b) ax+2y=6, substitute x=1, y=2 a(1)+2(2)=6 a+4=6 a=6-4 a=2 x+2y=a , substitute x=1, y=2 1+2(2)=a 1+4=a a=5 |
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Question (3):
Solve the following equation: 7x+5=3x-25 |
Answer:
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Question (4):
Solve the following equation: 5x-(3x-1)=x-4 |
Answer:
5x-(3x-1)=x-4 5x-3x+1=x-4 2x-x=-4-1 x=-5 |
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Question (5):
Solve the following equation:
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Answer:
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Question (6):
Solve the following equation:
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Answer:
 5(2-9x) = 4(15-4x) (by cross multiplication) 10-45 x= 60-16x -45x+16x=60-10 -29x=50  |
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Question (7):
Solve the following equation:
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Answer:
 5(3x+5) = 2(2x-1) (by cross-multiplication) 15x-4x = -2-25 11x = -27  |
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Question (8):
Solve the following equation:
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Answer:
2x-(1-2x) = 5-3(1+x) 2x-1+2x = 5-3-3x 4x+3x = 5-3+1 7x=3  |
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Question (9):
Solve the following equation:  |
Answer:
 4x + 7 = -3 (2x + 1) (By cross-multiplication) 4x+7=-6x-3 4x+6x=-3-7 10x=-10  x=-1 |
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Question (10):
Solve the following equation:
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Answer:
      x=2 |
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Question (11):
Solve the following equation:
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Answer:
   2y-15=180 2y=180+15 2y=195  |
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Question (12):
Solve graphically x - 2y = 1 and x + y = 4. Use 2cm = 1 unit on both axes and plot only 3 points per line. |
Answer:
x - 2y = 1 2y = x - 1   x + y = 4 y = 4 - x 
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Question (13):
Use a graph paper for this question. Draw the graphs of 2x-y-1 = 0 and 2x + y = 9 on the same axes. Use 2cm = 1unit on both the axes and plot only three points per line. Write down the co-ordinates of the point of intersection of the two lines. |
Answer:
2x - y - 1 = 0 y = 2x - 1  2x + y = 9 y = 9 - 2x 
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Question (14):
Solve graphically x + y + 2 = 0 and 3x - 4y = 5. Take 2 cm=1 unit.Write down the co-ordinates of the point of intersection of the two lines. |
Answer:
a) x + y + 2 = 0 y = - x - 2  b) 3x - 4y = 5 4y =3x - 5  
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Question (15):
Draw the graph of: (i) x = 5 (ii) x + 5 = 0 (iii) y = 7 (iv) y + 7= 0 |
Answer:
i) x = 5 ii) x + 5 = 0 x = -5 iii) y = 7 iv) y + 7= 0 y = -7
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Question (16):
Use the table given below to draw the graph. From the graph, find the values of 'a' and 'b', state the linear equation between the variables x and y.
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Answer:
a = 0 b = 3 Linear equation 2y = x + 1 Ans: i) a=0, b=3 ii) a = -1, b = 3 ii) 2y = x + 1
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Question (17):
Draw the graph of 2x - y = 4. |
Answer:
2x - y = 4 y = 2x - 4 
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Question (18):
Draw the graphs of the following equations i) x + 3 = 0 ii) y - 3 = 0 iii) 2x + 3y = 12 Write down the co-ordinates of the triangle formed by these lines. |
Answer:
i) x + 3 = 0 x = -3 ii) y - 3 = 0 y = 3 iii) 2x + 3y = 12 3y = 12 - 2x  
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Question (19):
Solve graphically x = 4 and 3x - 2y = 10. |
Answer:
A) x = 4 B) 3x - 2y = 10 2y = 3x - 10  
 Ans : x = 4; y = 1 |
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Question (20):
Show graphically that the system of linear equations 2x+4y=10 and 3x + 6y = 12 has no solution. |
Answer:
2x + 4y = 10 4y = 10 - 2x   3x + 6y = 12 6y = 12 - 3x  
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