** 4. LINEAR EQUATIONS IN TWO
VARIABLES**

Hi friends and my dear students! In this post, I have covered **Important questions
for 10 ^{th} class maths chapter-4 **

**LINEAR EQUATIONS**

**, Chapter wise previous year Questions.**After Reading Please do share it with your friends.

**Learn Maths for All Classes here.**

PRIORITY-I

**1 MARK QUESTIONS: **

1. Write the general form of linear equation in two
variables and write condition?

2. Solve 2(x+3) = 18?

3. Find ‘x’ which satisfies the equation 2x-(4-x) = 5-x?

4. Check whether the pair of linear equations 2x+y-5 = 0
and 3x-2y-4 = 0 interesting, parallel, or coincident lines?

5. Check whether the pair of linear equations 3x+4y = 2
and 6x+8y = 5 interesting, parallel, or coincident lines?

6. Check whether the pair of linear equations 2x-3y = 5
and 4x-6y =15 are consistent?

7. Represent the following situations as linear equations form :

i) The number of skirts is two less than twice the number of pants purchased. Also the number of skirts is four less than four times the number of pants purchased.

ii) The number of girls is 4 more than the number of boys

**2 MARKS QUESTIONS **

8.
For what value of p, the equations 2x+py = -5 and 3x+3y = -6 have a unique
solution?

10.
Check the equation i. x+2y=5, 3x+4y=20 ii. x+y=2, 2x+2y=4 are consistent or not

11. If px+3y-(p-3)=0, 12x+py-p=0
has infinite solutions then find ‘p’?

12. Find the value of k, the equations 2x-ky+3=0 and 4x+6y-5=0 represent parallel lines?

13.
For what value of k, the equations 3x+4y+2=0 and 9x+12y+k=0 represent
coincident lines?

14.
5pencils and 7pens together cost Rs.50, where as 7pencils and 5pens together
cost Rs.46. write pair of linear equations to find the cost of 1 pencil and
that 1 pen?

15.
The larger of two supplementary angles exceeds the smaller by 18°. Find the
angles?

16.
Two angles are complementary. The larger angle is 3° less than twice the
measure of the smaller angle. Find the measure of each angle.

17.
Solve i) 3x+2y=11 and 2x+3y=4 ii) 3*x *+ 4*y *= 25, 5*x *- 6*y
*= -9 by elimination method?

18.
Half the perimeter of a rectangular garden, whose length is 4m more than its
width, is 36m.Find the dimensions of the garden

19.
Solve i)0.2*x *+ 0.3*y *= 13, 0.4*x *+ 0.5*y *= 2.3 ii) 3*x
*- 5*y *= -1, *x *- *y *= - 1by substitution method

**Also Check**

Important questions for 10th class maths chapter-5 Quadratic-equations

**Introduction to Knowing Our Numbers Key Points**

**SSC (10th class) Trigonometry Exercise - 11.1 Solution**

**SSC(10th class) Trigonometry Exercise - 11.1 Solutions**

**4 MARKS QUESTIONS **

1. In a garden there are some
bees and flowers. If one bee sits on each flower, one bee will be left. If two
bees sit on each flower, one flower will be left. Find the number of bees and
flowers?

and 2 /√ x+3/√ y =2 4/√ x-9/√ y =-1

3.
The perimeter of rectangular plot is 32m.If the length is increased by 2m and
the breadth is decreased by 1m, the area of plot remains same. Find the length
and breadth of plot?

4.
The sum of a two digit number and the number obtained by reversing the digit is
66. If the digits of the number differ by 2, find the number. How many such
numbers are there?

5.
A boat goes 30km upstream and 44km downstream in 10hrs in 13hrs it can go 40km
upstream and 55km downstream. Determine the speed of the stream and that of the
boat in still water.

6.
A chemist has two solutions of hydrochloric acid in stock. One is 50% solution
and the other is 80% solution how much of each should be used to obtained 100ml
of a 68% solutions

7.
The ratio of incomes of two persons is 9:7 and the ratio of their expenditures
is 4:3 if each of them manages to save 2000 per month find their monthly
income?

8. Tabita went to a bank to
withdraw Rs.2000. she asked the cashier to give the cash in Rs.50 and Rs.100
notes only. She got 25 notes in all. How many notes each of Rs.50 and Rs.100
she received?

10.
A fraction becomes 4/5, if 1 is added to both numerator and denominator. If,
however, 5 is subtracted from both numerator and denominator, the fraction
becomes 1/2. What is the fraction?

11.
A man travels 370 km partly by train and partly by car. If he covers 250 km by
train and the rest by car, it takes him 4 hours. But if he travels 130 km by
train and the rest by car, it takes 18 minutes more. Find the speed of the
train and that of the car.?

12. 2 women and 5 men can together finish an embroidery work in 4 days while 3 women and 6 men can finish it in 3 days. Find the time taken by 1 woman alone and 1 man alone to finish the work.

13. The area of a rectangle gets reduced by 80 sq units if its length is reduced by 5 units and breadth is increased by 2 units. If we increase the length by 10 units and decrease the breadth by 5 units, the area will increase by 50 sq units. Find the length and breadth of the rectangle.

14. Solve 2/x+ 3/y = 13 and 5/x- 4/y =-2

15. Solve 5 / x +y -2/x-y =-1and 15/ x+ y -7/x -y =-10

16. Solve

5 /
x -1 +1/y-2 = 2 and 6 / x -1 -3/y-2 = 1

17. solve x +y/xy = 2 and x-y/xy =-6and

18.
Solve 6x+3y=6xy and 2x+4y=5xy

19.
Solve 2x+3y = 1 and 3x-y = 7 graphically?

20.
Solve 3x+2y = 5 and 2x-2y = 7 graphically?

21. Solve 2x-3y = 8 and 4x-6y =
9 graphically?

Also Check

**Important questions for 10th class maths chapter-1 Real numbers**

Important questions for 10th class maths chapter-3 polynomial

**PRIORITY-II**

**1 MARK QUESTIONS: **

1.
What is the value of ‘a’ for which (3, a) lies on 2x-3y=5?

2.
Write the number of solutions of the following pair of linear equations
x+3y-4=0, 2x+6y=7?

3.
If a pair of linear equations in two variables is consistent, then which lines
are represented by two equations?

4.
Comment on the solution of dependent pair of linear equations.

5.
Write the possible situations when two lines are drawn in the same plane?

6.
What is the solution set of inconsistent equations?

7.
The larger of two complementary angles is double the smaller. Find the angles

8. Is a dependent pair of
linear equations always consistent? Why or why not?

9. If two supplementary angles
are in the

ratio
1:3, then find the angles

10.
2 tables and 3 chairs together cost Rs 2000/- whereas 3 tables and 2 chairs
together cost Rs 3000/-. Form the appropriate pair of linear equations for this
situation.

11.
The coach of a cricket team bus 3 bats and 6 balls for Rs 3900/-. Later he buys
another bat and 3 more balls for Rs 1300/- of same kind. Represent this
situation algebraically

12.
In a class of 40 students, number of girls is 10 greater than number of boys.
Connect this situation algebraically by linear equation.

13.
Write two linear equations such that they form parallel and intersecting lines
with line representing 2x+3y-8=0.

** 2 MARKS QUESTIONS **

14.
For what value of ‘k’, the system of equations 2x + ky = 10, 3x+ (k+3) y=12 are
parallel.

15.
Write the value of ‘k’ for which the system of equations x+y-4=0 and 2x+ky-3=0
has no solution.

16.
If the system of equations 3x+y=1, (2k-1)x+(k-1)y=2k+1 is inconsistent, then
find ‘k’.

17.
Check whether the pair of linear equations 2x+y-5=0 and 3x-2y-4=0 are
intersecting, parallel or coincident lines?

18. For what value of ‘k’, the
system of equations x-ky=2, 3x+2y=-5 has a unique solution.

**4 MARKS QUESTIONS**

1.10/x+y+2/x-y=4 and 15/x+y-5/x-y=-2

2. 3/x+y+2/x-y=2 and 9/x+y-4/x-y=1

3. 1/x+y+1/x-y=3/4 and 1/2(3x+y)- 1/2(3x-y)=-1/8

4. Solve x+y=a+b, ax-by=a^{2}-b^{2} using
method of elimination.

5. Rahim travels 600 km to his home partly by train and partly by car. He takes 8 hours if he travels 120 km by train and rest by car. He takes 20 minutes more if he travels 200 km by train and rest by car. Find the speed of the train and the car

6. In a competitive exam, 3 marks are to be awarded for every correct answer and for every wrong answer, 1 mark will be deducted. Madhu scored 40 marks in this exam. Had 4 marks been awarded for each correct answer and 2 marks deducted for each incorrect answer, Madhu would have scored 50 marks. How many questions were there in the test? (Madhu attempted all the questions)

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