LInear equations in two variables

The pair of linear equations 2x + 3y = 5 and 4x + 6y = 10 is

• (a) inconsistent

• (b) consistent

• (c) dependent consistent

• (d) none of these

The pair of equations y = 0 and y = –7 has

• (a) one solution

• (b) two solutions

• (c) infinitely many solutions

• (d) no solution

The pair of equations x = a and y = b graphically represents lines which are

• (a) parallel

• (b) intersecting at (b, a)

• (c) coincident

• (d) intersecting at (a, b)

The pair of equations x = 4 and y = 3 graphically represents lines which are

• (a) parallel

• (b) intersecting at (3, 4)

• (c) coincident

• (d) intersecting at (4, 3)

a₁x + b₁y + c₁ = 0 and a₂x + b₂y + c₂ = 0, where a₁, b₁, c₁, a₂, b₂, c₂ are all real numbers and a₁² + b₁² ≠ 0, a₂² + b₂² ≠ 0, is called a

• (a) family of two different straight lines

• (b) family of two coincident lines

• (c) pair of linear equations in two variables

• (d) none of these

A pair of linear equations which has a unique solution x = 2, y = –3 is

• (a) x + y = –1; 2x – 3y = –5

• (b) 2x + 5y = –11; 4x + 10y = –22

• (c) 2x – y = 1 ; 3x + 2y = 0

• (d) x – 4y – 14 = 0; 5x – y – 13 = 0

If x = a, y = b is the solution of the pair of equations x – y = 2 and x + y = 4, then the respective values of a and b are

• (a) 3, 5

• (b) 5, 3

• (c) 3, 1

• (d) –1, –3

The pair of equations ax + 2y = 7 and 3x + by = 16 represent parallel lines if

• (a) a = b

• (b) 3a = 2b

• (c) 2a = 3b

• (d) ab = 6

Find the number of solutions of the following pair of linear equations:

x + 2y – 8 = 0

2x + 4y = 16

• no solutions

• Unique solutions

• infinite many solutions

• None of the above

Write whether the following pair of linear equations is consistent or not.

x + y = 14,

x – y = 4

• inconsistent

• consistent