CLASS 9

1. Coordinate Geometry
Linear equations in two variables
ax+by+c=0

2. 3x−y=7……..(1)
2x+3y=1…….(2)
Answer the questions based on above linear equations in two variables.
(a) Linear equations in two variables graph is always ……………. Line.
(b) Coefficient of x in eq(1) is a=….and in eq(2) is a= …..
(c) Coefficient of y in eq(1) is b=….and in eq(2) is b=…..
(d) Constant term in eq(1) is c=…. and in eq(2) is c= …..
(e) Value of y in equation (1) is ….. if x=0
(f) Value of y in equation (1) is ……… if x=1
(g) Value of y in equation (2) is ……… if x=0
(h) Value of y in equation (2) is ……… if x=-1
(i) Value of y in equation (1) is ……… if x=-1
straight
3 2
-1
7 1
3
-7
-4
1/3
1
-10

3. GRAPH OF GIVEN EQUATIONS
3x−y=7……..(1)
2x+3y=1…….(2)
INTERSECTION POINT

4. FIND THREE SOLUTION OF EACH EQUATION AND DRAW GRAPH 4x-3y+4=0,
⇒ 4x-3y+4=0---(1)
⇒ 4𝒙 = −𝟒 + 𝟑𝒚
⇒ 𝒙 =
−𝟒+𝟑𝒚
𝟒
1. PUT y =0
⇒𝒙 =
−𝟒+𝟑 ×𝟎
𝟒
⇒ x=- 4/4=-1
(-1, 0)
2. PUT y=1
⇒𝒙 =
−𝟒+𝟑 ×𝟏
𝟒
⇒ 𝒙 =
−𝟒+𝟑
𝟒
=
−1
4
(-0.25, 1)
3. PUT y=4
⇒𝒙 =
−𝟒+𝟑 ×𝟒
𝟒
⇒ 𝒙 =
−𝟒+𝟏𝟐
𝟒
=
8
4
= 2
(2, 4)
4. PUT y=-4
⇒𝒙 =
−𝟒+𝟑 ×−𝟒
𝟒
⇒ 𝒙 =
−𝟒−𝟏𝟐
𝟒
=
−16
4
=-4
(-4, -4)
X -1 -0.25 2 -4
y 0 1 4 -4

5. Solve of the following systems.
2x+4y=−10 and 6x+3y=6
2x+4y=−10
⇒ x+2y=-5 ---(1)
⇒ 𝒙 = −𝟓 − 𝟐𝒚
1. PUT y =0
⇒ 𝒙 = −𝟓 − 𝟐 × 𝟎
⇒ 𝒙 = −𝟓
(-5,0)
2. PUT y =1
⇒ 𝒙 = −𝟓 − 𝟐 × 𝟏
⇒ 𝒙 = −𝟓 − 𝟐 = −𝟕
(-7,1)
3. PUT y =-1
⇒ 𝒙 = −𝟓 − 𝟐 × −𝟏
⇒ 𝒙 = −𝟓 + 𝟐 = −𝟑
(-3,-1)
6x+3y=6
⇒ 2x+y=2 ---(2)
⇒ y= 𝟐 − 𝟐x
1. PUT x =0
⇒ y= 𝟐 − 𝟐x
⇒ y= 𝟐 − 𝟐 ×0
⇒ y= 𝟐
(0,2)
2. PUT x =1
⇒ y= 𝟐 − 𝟐x
⇒ y= 𝟐 − 𝟐 × 𝟏
⇒ y= 𝟐 − 𝟐 =0
(1,0)
1. PUT x =2
⇒ y= 𝟐 − 𝟐x
⇒ y= 𝟐 − 𝟐 × 𝟐
⇒ y= 𝟐 − 𝟒 = −𝟐
(2,-2)
X -5 -7 -3
y 0 1 -1
X 0 1 2
y 2 0 -2

6. X -5 -7 -3
y 0 1 -1
X 0 1 2
y 2 0 -2
(-5,0)
(-7,1)
(-3, -1)
(0,2)
(1, 0)
(2, -2)
Intersection point
(3, -4)

7. Draw the graphs of the pair of equations x + 2y = 5 and 2x-3y = – 4. Also find the points
where the lines meet the x-axis.

8. Determine graphically whether the following pair of linear equations
2x – 3y = 5; 3x + 4y = – 1

10. HOME WORK
1. Find the points where the graph of the equation 3x+4y=12 cuts the
x-axis and y axis.
2. Write the coordinates of the vertices of a rectangle, whose length
and breadth are 6 units and 3 units respectively. One vertex at
origin, the longer side lies in the y-axis and one vertex lies in the
second quadrant. Also, find the area of the rectangle.