MATHEMATICS CLASS X

LINEAR EQUATIONS

= <= span style=3D'mso-spacerun:yes'> =

= &nb= sp; = QUESTION BANK

<= /p>

I. Solve the following system of equations graphically

1. = x-2y =3D 2 ; &= nbsp; 3x+ 5y=3D17

2. = 2x+4y =3D10 ; 3x+= 6y =3D12

3. = x-2y=3D5 &= nbsp; ; &= nbsp; 2x-4y =3D10

4. = x+y =3D3 = ; &= nbsp; 2x+5y =3D12

5 &= nbsp; 3x+y+1=3D0 ;&n= bsp; 2x-y+8 =3D0

6. 4x – 5y -20 =3D0 &= nbsp; ; 3x + 5y = -15 =3D 0

II. Solve the system= of equations

1. = 3x+2y=3D-25 ; &= nbsp; -2x-y=3D10

2. = x + 2y =3D_{=
; &=
nbsp; 2x+y=3D}

3. = x+2y=3D-1 &= nbsp; ; &= nbsp; 2x-3y=3D12

4. = _{&=
nbsp; ; &=
nbsp; 2x–y=3D4}

5. = 3x–5y=3D19 ; &= nbsp; 3y-7x=3D-1

6. = 8x+5y=3D9 &= nbsp; ; &= nbsp; 3x+2y=3D4

7. = 7x+11y=3D1 ; &= nbsp; 8x+13y=3D2

8. = 3x+4y=3D24 ; &= nbsp; 20x-11y=3D47

9. = 4x-3y=3D8 &= nbsp; ; &= nbsp;

10. 2x+7y= =3D11 ; &= nbsp; -3x+5y=3D-1

11. _{=
; &=
nbsp;}

12.       _{=
    &=
nbsp;   ;        &=
nbsp;}

13. ax+by= =3D1 &= nbsp; ; &= nbsp; _-1

14. 2( ax-by) = + (a + 4b) =3D 0 := 2( b= x+ ay) + ( b -4 a) =3D0

15. 47 x + 31 y =3D63 = : &nbs= p; 31x +47 y =3D15 (CBSE = 2006)

16. = ax – by =3D 2ab

(CBSE 2006)

III. In ea= ch of the following systems of equations check whether the system has a unique solution or no solution or infinitely many solutions

1. = 7x-2y=3D3 = &nb= sp; 2. &nbs= p; 6x +5y =3D11 = 3. &nbs= p;

        &= nbsp;   _{=
            &nb=
sp;
    9x +
7.5y=3D21        =

      3x-5y=3D7}

4. = 4x+7y=3D10 &= nbsp; 5.= = -3x+4y=3D5 = = 6. =

              &= nbsp;         _{&=
nbsp;           &nbs=
p;     _{=
            &nb=
sp;    x-2y=3D2}}

7        &= nbsp; _{=

      =
8.         =
10x+y=3D9        =

     9.         =
4x-y=3D7}

&n= bsp; 2x-y=3D4 = &nb= sp; _{=
&=
nbsp;}

IV. Find the value of k for which the system has a unique solution

1. = 7x-2y=3D3 &= nbsp; &nbs= p; 2. = 2x+ky=3D1 = = 3. = 2x +3y -5=3D0

22x-ky=3D8 = &nb= sp; = 3x-5y=3D7 &= nbsp; &nbs= p; &= nbsp; kx-6y-8=3D0

V. For what value of k, will the following system of equations have infinite numbe= r of solutions.

1. = 3x+4y+2=3D0 &= nbsp; 2. = 2x-3y+5=3D0 3. (k-1)x+(k+2)y=3Dk

= 9x+12y+k=3D0 = = &nb= sp; 8x-ky+20=3D0 = = 2x+5y=3D3

4. = 2x-3y=3D7 &= nbsp; &nbs= p; &= nbsp; 5. = 2x+3y=3D2 &= nbsp; &nbs= p;

(k+2)x-(2k+1)y=3D3(2k-1) = (k+2)x+(2k+1)y=3D2(k+1)

VI. For what value of k, will the following system of equations have no solution?

1. = 2x + ky=3D11 = 2. = 9x + 4y=3D9 = ; &n= bsp; 3. = 8x+5y=3D9

5x-7y=3D5 = &nb= sp; 7x + ky=3D5 = = kx+10y=3D15

4. = kx+3y=3D3 &n= bsp; = ; 5. = 3x+y=3D1

2x+ky=3D6 = &nb= sp; (2k-1)x+(k-1)y=3D2k+1<= /p>

VII. Find the va= lue of p and q for which the following system of linear equations has infinite number of solutions

1. = 2x+3y=3D7 &= nbsp; &nbs= p; 2. = 2x+3y=3D7

2px+(p+q)y=3D28 = (p+q)x +2(p-q)y=3D21

VIII. Problems on simultaneous equations

= =

1. The s= um of two numbers is 58. The greater number exceeds twice the smaller number by 1. Find the numbers.

2. The s= um of the present age of Suresh and his mother is 89 years. After 11 years, mother’s age will be twice Suresh’s age. Find their present age= s

3. A man= sold a chair and a table for Rs.1520 there by making a profit of 25% on chair and = 10% on table. By selling them together for Rs.1535, he would have made a profit of 10% on the chair and 25% o= n the table. Find the cost of each.

4. The p= erimeter of a rectangle is 44cm. Its length exceeds twice its breadth by 4cm find the length and breadth of the rectangle.

5. Last = year one kilogram of tea and three kilograms of sugar together cost Rs.96. This year= the rates of tea increased by 15% and that of sugar by 10%. So the same amounts= of tea and sugar now cost Rs.108.60. Find the rates of tea and sugar per kilog= ram last year.

6. The s= um of the digits of a two digit number is 10. The number obtained by reversing the order of the digits of the given number exceeds the given number by 36. Find the given number.

7. A boa= t goes 30 km upstream and 44 km downstream in 10 hours. In 13 hours it, can go 40 = km up stream and 55 km downstream determine the speed of the stream and of the boat in still water

8. In a = _{ÐA
=3D x^o, =
ÐB
=3D (3x-2)^o and ÐC =3D y^o. Also ÐC - ÐB
=3D 9^o. Determine the three angles.}

9 A part= of monthly hostel charges in a college are fixed and the remaining depend on t= he number of days one has taken food in the mess. When a student A takes food = for 20 days, he has to pay Rs.1000 as hostel charges where as a student B takes food for 26 days, pays Rs.1180 as hostel charge. Find the fixed charge and = the cost of food per day.

10 The n= umerator of a fraction is 4 less than its denominator if the numerator is deceased b= y 2 and denominator is increased by 1 then denominator is eight times the numerator, find the fraction

11. 90% = and 97% pure acid solutions are mixed to obtain 21 liters of 95% pure acid solution= s. Find the amount of each type of acid to be mixed to form the mixture.

Hint Let x ltr of 90% pure a= cid solution and y ltr of 97% pure acid solution be taken.

&= nbsp; Then

12. A pe= rson invested some amount at the value of 12% simple interest and some other amo= unt at the rate of 10% simple interest. He received yearly interest of Rs.130 b= ut if he had inter changed the amounts invested he would have received Rs. 4 m= ore as interest. How much amount did he invest at different rates.

13. The = incomes of A and B are in the rate 3:4 and their expenditures are in the ratio of 5= :7. If each leaves Rs.1000 find their incomes.

&= nbsp; Hint 3x-5y=3D1000 &= nbsp; ; &= nbsp; 4x-7y=3D1000

14. In a= DABC one of the angles is 50% more than the sum of the other two angles. Find the largest angle.

15. Two = years ago, a father was five times as old as his son. Two years later , his age w= ill be 8 more than three times the age of the son. Find the present ages of fat= her and son.

&nb= sp;

16. A man travels a distance of 300 km at a uniform speed. If the speed of the train = is increased by 5 km an hour , the journey would have taken 2 hours less. Find= the original speed of the train. (CBSE 2006)

17. Find = the value of k so that the following system of equations has infinite solutions:3x-y-5=3D0; 6x-2y=3Dk=3D0 = ( CBSE 2008)

18. Repre= sent the following system of linear equations graphically. From the graph, find = the points where the lines intersect y axis. 3x+ y-5=3D0 ; 2x-y-5=3D0 ( CBSE 20= 08)

&nb= sp;

&= nbsp; ANSWERS

1. = (4,1) &= nbsp; 2.No solution = ; 3.infinite number of solution

= 4. x=3D1 , y=3D2 = 5. = x=3D-1, y =3D 2 = 6. x=3D5 y=3D0

1.         = x=3D5y =3D -2      &= nbsp; 2.         = _{&=
nbsp;           &nbs=
p;    3.         =
(3,-2)}

4. = (4,4) &= nbsp; 5 &= nbsp; (-2,-5) &= nbsp; &nbs= p; 6 &= nbsp; (-2,5)

7 &= nbsp; (-3,2) &= nbsp; 8 &= nbsp; (4,3) &= nbsp; &nbs= p; 9 &= nbsp;

10 (2,1) &= nbsp; 11 x=3Da , y=3Db &n= bsp; = ; 12 (8,-1)

13.       _{=

14.   (-1/2, 2)     15.}

III

1 unique= &= nbsp; &nbs= p; &= nbsp; 2 no solution &n= bsp; 3 no solution

4 infini= tely many &nb= sp; = 5 no solution = ; <= /span>6 unique solution

7 unique= &= nbsp; &nbs= p; &= nbsp; 8 infinitely many &nbs= p; 9 no solution

1.         = K_{_{&=
nbsp;           &nbs=
p;      2        &=
nbsp; K_{&=
nbsp;           &nbs=
p;    3        &=
nbsp; K}}}

1. = K=3D6 &= nbsp; &nbs= p; 2. = K=3D12 = 3 &= nbsp; K=3D3

4. = K=3D4 = 5. = K=3D4

1.         = K=3D-_{&=
nbsp;           2.=
         =
K=3D_{&=
nbsp;           &nbs=
p; 3.         =
K=3D16}}

4. = K=3D-6 &= nbsp; &nbs= p; 5. = K=3D2

VII

1. = 39, 19 = 2. = 26, 63 &nb= sp; 3. = 600, 700

4. = l=3D16cm, b =3D6cm 5. = 6hours, 20minutes &nbs= p; &= nbsp; 5 &= nbsp; 60,12

6. = 37 = 7. = boat 8km/hr stream 3 km/hr = 8. 25^=
o, 73^o, 82^o

9        &= nbsp; 400, 30            &nb= sp;          10.       _{=
            &=
nbsp;           &nbs=
p;          11     x=3D6, &n=
bsp;   y=3D15    12.       500 at 12% and 700 at 10%      13        6000
; 8000            &=
nbsp;    14        108}

15. son = =3D 10 yrs Father =3D 42 yrs

&n= bsp; = ; =

&n= bsp; = ; &n= bsp; &= nbsp; &nbs= p; &= nbsp; &nbs= p;