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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
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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
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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
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Answer:
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Question (4):
Solve the following equation:
5x-(3x-1)=x-4
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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:
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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.
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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.
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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.
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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
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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.
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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.
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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.
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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.
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Answer:
2x + 4y = 10
4y = 10 - 2x
3x + 6y = 12
6y = 12 - 3x
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Question (21):
Solve graphically:
3x + y + 1 = 0 and 2x - 3y + 8 = 0.
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Answer:
a) 3x + y + 1 = 0
y = -3x - 1
b) 2x - 3y + 8 = 0
3y = 2x + 8
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Question (22):
Find graphically, the vertices of the triangle whose sides are y = x + 5, y = -x and x = 3. Also find the area of the triangle.
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Answer:
a) y = x + 5
b) y = -x
c) x = 3
Vertices of D ABC are:
A (-2.5, 2.5)
B (3, 8)
C (+3, -3)
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Question (23):
Solve graphically
y = 2x - 6 and y = -2x + 10.
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Answer:
a) y = 2x - 6
b) y = -2x + 10
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Question (24):
Solve graphically the vertices of the triangle of sides 2y + x = 0, 3y = x and x = 6. Also find area of the triangle.
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Answer:
a) 2y + x = 0
2y = -x
b) 3y = x
c) x = 6
Vertices of DABC are:
A (0,0), B (6,2), C (6,-3)
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Question (25):
Solve graphically:
3y = 5 - x and 2x = y + 3.
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Answer:
1) 3y = 5 - x
2) 2x = y + 3
y = 2x - 3
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Question (26):
Solve graphically:
x + y = -1 and y - 2x = -4.
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Answer:
a) x + y = -1
y = -x -1
b) y - 2 x = -4
y = 2x - 4
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Question (27):
Which of the following equations have x=2, y=3 as solution ?
(a) 2x+3y=8 (b) x-2y = -4 (c) 5x-2y = 4
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Answer:
(a) Substitute x=2, y=3 in 2x+3y=8
2(2)+3(3)=8
x = 2, y = 3 is not a solution .
(b) Substitute x=2, y=3 in x-2y=-4
(c) Substitute x=2m y=3 in 5x-2y=4
4=4
x=2, y=3 is a solution of 5x-2y=4
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Question (28):
Find atleast 3 solutions of :
(a) 2x+4y=12 (b) 3x+5y=10 (c) x+3y=6 (d) 2x-5y=8
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Answer:
(a) 2x+4y=12
2x=12-4y
 x=6, y=0; x=2, y=2 and x=+10, y=-2 are three
Solution of 2x+4y=12 .
(b) 3x+5y=10
5y=10-3x
x=0, y=2; x=5, y=-1 and x=-5, y=5 are three solutions of 3x+5y=10
(c) x+3y=6
x=6-3y
Put y=0, x=6
y=1, x=6-3 = 3
y=2, x=6-6 = 0
x=6, y=0; x=3 y=1; x=0, y=2 are solutions of x+3y=6
(d) 2x-5y=8
2x=8+5y
x=4, y=0; x=9, y=2; x=-1, y=-2 are solutions of 2x-5y=8
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Question (29):
Find the values of a so that x=1, y=2 is a solution of:
(a) 3x-ay=5 (b) ax-5y=17 (c) 3x+2ay=11
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Answer:
(a) 3x-ay=5
substitute x=1, y=2
3(1)-a(2)=5
3+5=2a
a=4
(b) ax-5y=17
substitute x=1, y=2
a(1)-5(2)=17
a-10 = 17
a = 27
(c) 3x+2ay=11
substitute x=1, y=2
3(1)+2a(2)=11
3+4a=11
4a=11-3
4a=8
a=2
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Question (30):
Solve the following equation:
8x=20+3x
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Answer:
8x=20+3x
8x-3x=20
5x=20
x=4
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