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Question (1):
Solve the following equation:
3(x-1)=8
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Answer:
3(x-1)=8
3x-3=8
3x=8+3
3x=11
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Question (2):
Solve the following equation:
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Answer:
54y-45=14 y
54y-14y=45
40y=45
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Question (3):
Solve the following equation:
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Answer:
2(3x-19)=10
3x-19 = 5
3x=5+19
3x=24
x=8
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Question (4):
Solve the following equation:
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Answer:
By cross-multiplication, we get
(8x-3) (x-2) = (4x+1) (2x+5)
8x(x-2)-3(x-2) = 4x(2x+5)+1(2x+5)
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Question (5):
Solve the following equation:
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Answer:
-58y-232 = -108y+18
-58y+108y = 18+232
50y=250
y=5
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Question (6):
Solve the following equation:
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Answer:
42y-42 = 35y-21
42y-91y = -21+42
-49y = 21
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Question (7):
Draw the graph of y=3.
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Answer:
The graph of y = 3 is a line parallel to the x-axis.
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Question (8):
Draw the graph of y=-4.
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Answer:
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Question (9):
Draw the graph of x+4=0.
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Answer:
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Question (10):
Draw the graph of y-6=0.
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Answer:
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Question (11):
Draw the graph of 3x+2y=6.
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Answer:
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Question (12):
Draw the graph of 3x-2y=9.
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Answer:
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Question (13):
Draw the graph of 3x+y=12.
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Answer:
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Question (14):
Draw the graph of 2x-3y=12. Use the graph to find the slope of line and area between the axes.
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Answer:
2x-3y=12
2x=12+3y
y=0, x=6
y=-2, x=3
y=-4, x=0
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Question (15):
Draw the graph of 2x+y=5. Use the graph to find the slope of line and area between the axes.
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Answer:
2x+y=5
y=5-2x
x=0, y=5
x=2, y=1
x=3, y=-1
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Question (16):
Draw the graph of 4x+3y-6=0.
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Answer:
4x+3y-6=0
3y=6-4x
x=0, y=2
x=3, y=-2
x=-3, y=6
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Question (17):
Solve graphically
2x-2=y; x+3y=15
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Answer:
2x-2=y
y=2x-2
At x=0, y=2(0)-2=-2
At x=1, y=2(1)-2=0
At x=2, y=2(2)-2=2
x+3y=15
x=15-3y
At y=5, x=15-3(5)=0
At y=4, x=15-(3)4=3
At y=6, x=15-3(6)=-3
x=15-3y
At y=5, x=15-3(5)=0
At y=4, x=15-(3)4=3
At y=6, x=15-3(6)=-3
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Question (18):
Solve graphically
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Answer:
x=4
x=4; is a line parallel to y axis.
3x+2y=10
3x=10-2y
Solution: x=4, y=-1
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Question (19):
Solve graphically
3y=5-x; 2x=y+3
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Answer:
3y=5-x
2x=y+3
3y=5-x
2x=y+3
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Question (20):
Solve graphically
3x+y+1=0; 2x-3y+8=0
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Answer:
3x+y+1=0
3x+y=-1
3x=-1-y
2x-3y+8=0
2x+8=3y
2x=3y-8
Solution: x=-1 and y=2
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Question (21):
Solve graphically
2y-x=9; 6y-3x=21
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Answer:
Plotting through points (1,5) (3,6) (5,7) and joining them by a ruler we get through line l.
Plotting through points (-3,2) (-1,3) and (3,5) and joining them, we get line m.
We shows that line 'l' and 'm' are parallel.
The two lines have no part in common. Hence given system of equation has no solution.
No solution as lines are parallel
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Question (22):
Solve graphically
x+y=-1; y-2x=-4
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Answer:
x+y=-1
y=-1-x
At x=-2, y=-1+2=1
At x=-3, y=-1+3=2
At x=0, y=-1-0=-1
y-2x=-4
y=2x-4
At x=1, y=2-4=-2
At x=-1, y=-2-4=-6
At x=0, y=0-4=-4
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Question (23):
Solve graphically
2x-3y-7=0; 2x+y-3=0
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Answer:
2x-3y-7=0
2x-3y=7
2x=7+3y
2x+y-3=0
y=3-2x
when x=0, y=3
when x=-1, y=5
when x=2, y=-1
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Question (24):
Solve graphically
-x+2y=6; 3x-6y=0
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Answer:
-x+2y=6
x=2y-6
At y=1, x=2-6=-4
y=2, x=4-6=-2
y=3, x=6-6=0
3x-6y=0
3x=6y
x=2y
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Question (25):
Solve graphically
2y-x=9; 6y-3x=21
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Answer:
2y-x=9
x=2y-9
6y-3x=21
3x=6y-21
x=2y-7
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Question (26):
Draw the graphs of 6y=5x+10; 5x-y-15=0. Also find the coordinates of the point of intersection and area of the triangle between the lines and x-axis.
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Answer:
6y=5x+10
5x-y-15=0
5x-15=y
x=0, y=-15
x=1, y=-10
x=2, y=-5
x=3, y=0
Co-ordinates of the point of intersection=(4,5)
=12.5 sq.units
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Question (27):
Solve graphically
x=-y and 3x=2y+10
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Answer:
x=-y
3x=2y+10
y=1, x=4
y=4, x=6
y=-2, x=2
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Question (28):
Solve graphically
x+2y-4=0, 3x=2y+4
Also find area of the triangle formed by the lines and the x-axis.
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Answer:
x+2y-4=0
x=4-2y
y=0, x=4
y=1, x=2
y=2, x=0
3x=2y+4
y=1, x=2
y=4, x=4
y=-2, x=0
Solution : x = 2, y = 1
=1.25 sq. units
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Question (29):
Draw the graph of 2y-x=7. Find the slope of the line. Determine whether (3,2) is a point on the line or not.
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Answer:
2y-x=7
2y-7=x
x=2y-7
y=0, x=-7
y=2, x=-3
y=3, x=-1
(3,2) is not a point on the graph.
Let (x1,y1)=(-7,0)
(x2,y2)=(-3,2)
m=0.5
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Question (30):
Draw the graph of 2x-3y=4. Is (8,4) a point on the line. Find y when x=-4.
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Answer:
2x-3y=4
2x=4+3y
y=0, x=2
y=2, x=5
y=-2, x=-1
(8,4) is a point on the graph. When x=-4, y=-4
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Question (31):
Draw the graph of x+6y=12. From the graph, find y when x=0.
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Answer:
x+6y=12
x=12-6y
y=1, x=6
y=2, x=0
y=3, x=-6
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