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Kamal Public Sr. Sec. School
Class IX – Maths
Linear Equation in two variables
Section – A
All questions are of one mark each.
2x  3 y  5
1
If
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3
4
5
Which type of solution exists in linear equation 5x-7=0, represented as ax+by+c=0?
Is x=7, y=-3 is a solution of 3x+y=19?
At which point the linear equation 3x+5y=6 cuts the x-axis at the point?
The point of the form (a,-a) always lies on the line
a) x=y
b) x+y=0
c) x-y=0
d) x=a
Under what conditions does the equation ax+by+c=0 represent a linear equation in two variables?
The graph of a linear equation 7x=5 is
a) parallel to y-axis
b) parallel to x-axis
c) lies along x-axis
d) passes through origin
For what value of k, x=2 and y=-1 is a solution of x+3y-k=0?
Any solution of linear equation 5x+0y=11 in two variables, is of the form
6
7
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a)
c)
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 11 
 ,0 
5 
7 
 ,  
5 
is written in standard form ax+by+c=1, then what are the values of a, b and c?
b)
is a real number
d)
 11 
 ,  
5 
 11 
 0, 
 5
is a real number
If x years, represent the present age of father and y year represent the present age of the son, then the
statement “present age of the father is 4 years more than 5 times the age of the son” in mathematical term
equation is
a) x-5y=4
b) x+5y=4
c) y-5x=4
d) y+5x=4
Section – B
All questions are of two marks each.
11
A three wheeler scooter charges ` 10/- for the first km and ` 4.50 each for every subsequent km.
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distance of x km, an amount of ` y is paid. Write the linear equation representing the above information.
Find four different solutions of equation x+2y=6.
Draw the graph of the equation : 3x-4y=12. From the graph, check whether x=4, y=2 is a solution or not?
Express x in terms of y, given that 3x+4y=6, check whether the point (3,2) is on the given line.
A part of monthly expenses of a family on milk is fixed which is ` 100/- and remaining varies with quantity of a
milk taken extra at the rate of ` 25/- per litre.
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All
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All
For a
Taking quantity of milk required as x litres and total
expenditure on milk as ` y, write a linear equation representing the above information.
Give geometric representation of equation 5x+15=0 in (i) one variable
(ii) two variables.
Section C
questions are of three marks each.
Draw graph of the equation 3x-4y=12. From the graph find the value of y, if x=8.
Draw the graph of two lines whose equations are 3x-2y+6=0 and x+2y-6=0 on the same graph paper. Also,
find the coordinates of the point whether the two lines intersect each other.
If the number of hours for which a labourer work is x and y are his wages (in rupees) and y=2x-1. Draw the
graph of work wages equation. From the graph, find the wages of the laborer if he works for 6 hours.
Draw the graph of 2x+7=3y. From the graph read the value of x when y=1.
Find two solutions for each of the following equations :a) 4x+3y=12
b) 2x+5y=0
c) 3y+4=0
Draw the graph of the equation 3x+y=6. Find the points where the line meets two axes.
Solve the following equation for x: 24-3(x-2)=x+18. Also represent the solution graphically in xy plane.
Section D
questions are of four marks each.
x
3x  2 4( x  1) 2

 (2 x  1)
7
5
3
24
Solve for
25
A and B are friends. A is elder to B by 5 years. B’s sister C is half the age of B while A’s father D is 8 years
older then twice the age of B. If the present age of D is 48 years, find the present age of A, B and C.
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Solve :
2 x  3 3x  1

2 x  1 3x  5
and represent this on xy plane.