Hg
Name: Class 10 Date:
___________________________________________________________________________________________________________________________________
___________________________________________________________________________________________________________________________________
The Hg Classes (8
th
to 12
th
) By: Er Hershit Goyal (B.Tech. IIT BHU), 134-SF, Woodstock Floors, Nirvana Country, Sector 50, GURUGRAM +91 9599697178.
fb.me/thehgclasses linkedin.com/company/the-hg-classes instagram.com/the_hg_classes g.page/the-hg-classes-gurugram thehgclasses.co.in
Linear Equations in two variables
1. Solve the following system of equations graphically: [CBSE 2008]
x + 3y = 6;
2x – 3y = 12
And hence find the value of a, if 4x + 3y = a.
OR
Solve the following system of linear equations graphically: [CBSE 2002]
2x – y – 4 = 0;
x + y + 1 = 0
Find the points where the lines meet y-axis.
2. Solve:
4
𝑥
+ 3y = 8;
6
𝑥
– 4y = -5 [CBSE 2010]
3. Solve:
5
(x−1)
+
1
(y−2)
= 2;
6
(x−1)
–
3
(y−2)
= 1 [CBSE 2009]
4. Solve: [CBSE 2005]
ax + by = (a - b)
bx – ay = (a + b)
OR
Solve:
x
a
+
y
b
= 2;
ax – by = a
2
- b
2
[CBSE 2005]
5. Find the values of p and q for which the following system of equations has infinite number of solutions:
2x + 3y = 7 [CBSE 2001]
(p + q)x + (2p - q)y = 21
6. For what value of k, will the system of equations x + 2y = 5 and 3x + ky – 15 = 0 has: **
(i) unique solution (ii) no solution? [CBSE 2001]
7. The sum of a 2-digit number and the number formed by interchanging its digits is 110. If 10 is
subtracted from the first number, the new number is 4 more than 5 times the sum of the digits in the
first number. Find the first number. [CBSE 2002]
Hg
Name: Class 10 Date:
___________________________________________________________________________________________________________________________________
___________________________________________________________________________________________________________________________________
The Hg Classes (8
th
to 12
th
) By: Er Hershit Goyal (B.Tech. IIT BHU), 134-SF, Woodstock Floors, Nirvana Country, Sector 50, GURUGRAM +91 9599697178.
fb.me/thehgclasses linkedin.com/company/the-hg-classes instagram.com/the_hg_classes g.page/the-hg-classes-gurugram thehgclasses.co.in
Answers:
1. 6,0; a=24
2. 0,-4; 0,-1
3. x=2, y=2
4. x=4, y=5
5. x=1, y=-1
6. x=a, y=b
7. p=5, q=1
8. (i) k is not equal to 6 (ii) no value of k exists
9. 64
