Question 21
Question: Solve graphically
2y-x=9; 6y-3x=21
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
Question 22
Question: Solve graphically
x+y=-1; y-2x=-4
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
Question 23
Question: Solve graphically
2x-3y-7=0; 2x+y-3=0
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
Question 24
Question: Solve graphically
-x+2y=6; 3x-6y=0
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
Question 25
Question: Solve graphically
2y-x=9; 6y-3x=21
Answer: 2y-x=9
x=2y-9
6y-3x=21
3x=6y-21
x=2y-7
Question 26
Question: 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.
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
Question 27
Question: Solve graphically
x=-y and 3x=2y+10
Answer: x=-y
3x=2y+10
y=1, x=4
y=4, x=6
y=-2, x=2
Question 28
Question: Solve graphically
x+2y-4=0, 3x=2y+4
Also find area of the triangle formed by the lines and the x-axis.
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
Question 29
Question: 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.
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
Question 30
Question: Draw the graph of 2x-3y=4. Is (8,4) a point on the line. Find y when x=-4.
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
Question 31
Question: Draw the graph of x+6y=12. From the graph, find y when x=0.
Answer: x+6y=12
x=12-6y
y=1, x=6
y=2, x=0
y=3, x=-6
