# General Form of a Pair of Linear Equations in Two Variables

## Trending Questions

**Q.**If the pair of linear equations a1x+b1y+c1=0 and a2x+b2y+c2=0, (a1, b1, c1, a2, b2 and c2 are all real numbers and a1, b1, a2, b2, are not equal to zero) represents parallel lines, then which of the following is correct?

- a1a2=b1b2≠c1c2

- a1a2≠b1b2

- a1a2=2b1b2=2c1c2

- a1a2=b1b2=c1c2

**Q.**In the equation ax+by+c=0, the line is parallel to x axis when a =

- 2
- 0
- 1

**Q.**The line ax+by+c=0, is parallel to x axis when a =

- 2
- 0
- 1

**Q.**What are the values of a, b and c for the equation y=0.5x+√7 when written in the standard form: ax+by+c=0 ?

- 0.5, 1, −√7
- 0.5, −1, √7
- −0.5, 1, √7
- 0.5, 1, √7

**Q.**If am â‰ bl, then the system of equations

$ax+by=c\phantom{\rule{0ex}{0ex}}lx+my=n$

(a) has a unique solution

(b) has no solution

(c) has infinitely many solutions

(d) may or may not have a solution

**Q.**

**Question 1 (ii)**

For which value(s) of λ does the pair of linear equations λx+y=λ2 and x+λy=1 have infinitely many solutions?

**Q.**Convert the following equations in the general form given by:

a1x+b1y+c1=0 and

a2x+b2y+c2=0,

and find a1, b2 and c2 respectively.

(1) 4x + 9y = 11

(2) 3x + 3y = 0

- 3, 3, 11
- 3, 3, -11
- 4, 3, 0
- 4, 3, 11

**Q.**

**Question 1 (iii)**

For what value(s) of λ, does the pair of linear equations λx+y=λ2 and x+λy=1 have a unique solution?

**Q.**Convert the following equations in the general form given by:

a1x+b1y+c1=0 and

a2x+b2y+c2=0,

and find a1, b2 and c2 respectively.

4x+9y=11

3x+3y=0

- 3, 3, -11
- 3, 3, 11
- 4, 3, 0
- 4, 3, 11

**Q.**

- True
- False

**Q.**

The value of x which satisfies following pair of linear equations is:

(i) x + 2y = -2

(ii) x - 2y = 12

5

7

-5

-7

**Q.**Two customers Shyam and Ekta are visiting a particular shop in the same week (Tuesday to Saturday). Each is equally likely to visit the shop on any day as on another day. What is the probability that both will visit the shop on different days?

OR

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

[3 Marks]

**Q.**If b=

- 1
- 2
- \N

**Q.**

Condition satisfied by the pair of equation 2x+3y=−5 and 4x+6y−10=0 is

a1a2 ≠ b1b2 = c1c2.

a1a2 = b1b2 = c1c2

a1a2 = b1b2 ≠ c1c2

a1a2 ≠ b1b2

**Q.**Given a linear equation 2x+3y=10. How many pairs of solution (x, y) are possible such that x and y (≥0) both are integers?

- 1
- 3
- 4
- 2

**Q.**Question 2 (iii)

Form the pair of linear equations in the following problems, and find their solutions (if they exist) by the elimination method:

The sum of the digits of a two-digit number is 9. Also, nine times this number is twice the number obtained by reversing the order of the digits. Find the number.

**Q.**If a point (1, 2) lies on the line represented by the equation 3y=ax+7, then the value of a is

−1

- 1
- 2

**Q.**

Which of the following are Pair of Linear Equation in two variables?

2x + y = 2; 3x - z=2

12x + 4y + 3 = 0; 4x + 4y + 4 = 0

x + 2 = 0; a + 2b = 0

x + y - 3 = 0; 4a + 2b + c = 24

**Q.**Convert the following equations in the general form given by:

a1x+b1y+c1=0 and

a2x+b2y+c2=0,

and find a1, b2 and c2 respectively.

4x+9y=11

3x+3y=0

- 3, 3, -11
- 4, 3, 0
- 3, 3, 11
- 4, 3, 11

**Q.**The graph for the linear equation given below

**Q.**

Condition satisfied by the pair of equation 2x+3y=−5 and 4x+6y−10=0 is

≠ = .

= =

= ≠

≠

**Q.**Which of the following is/are an equation?

- x=y
- x=0
- y=0
- None of the above

**Q.**Solve for x and y:

0.4x+0.3y=1.7,

0.7x−0.2y=0.8.

**Q.**If the system of equation, a2x−ay=1−a & bx+(3−2b)y=3+a possesses a unique solution x=1, y=1 then:

- a=1, b=1
- a=−1, b=1
- a=0, b=0
- None of the above

**Q.**If a point (1, 2) lies on the line represented by the equation 3y=ax+7, then the value of a is

−1

- 1
- 2

**Q.**

Which of the following are Pair of Linear Equation in two variables?

2x+y=2;3x−z=2

12x+4y+3=0;4x+4y+4=0

x+2=0;a+2b=0

x+y−3=0;4a+2b+c=24

**Q.**Divide 80 into two numbers, such that 5 times one number is equal to 3 times the other number.

- 30 and 50
- 35 and 52
- 40 and 60
- 22 and 49

**Q.**ax+by-c=0 is the generic form of linear equation in two variables.

- False
- True

**Q.**Based on equations reducible to linear equations

Solve for x and y: 9+25xy=53x and 27−4xy=x

- x=1, y=4
- x=2, y=7
- x=6, y=2
- x=3, y=2

**Q.**

Condition satisfied by the pair of equation 2x+3y=−5 and 4x+6y−10=0 is

a1a2 ≠ b1b2 = c1c2.

a1a2 = b1b2 = c1c2

a1a2 = b1b2 ≠ c1c2

a1a2 ≠ b1b2