Pair of Linear Equations in Two Variables Test

Result

Pair of Linear Equations in Two Variables Test - 7

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Question 1
1 / -0

If a pair of linear equation is consistent, then the lines will be

A
intersecting or coincident

B
parallel

C
always intersecting

D
always coincident

Solution

If a consistent system has an infinite number of solutions, it is dependent. When you graph; the equations, both equations represent the same line. So for consistent line it has to be parallel or even they intersect at one point. If a system has no solution, it is said to be inconsistent. The graphs of the lines do not intersect, so the graphs are parallel and there is no solution.
Question 2
1 / -0

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

A
intersecting at (a, b)

B
parallel

C
coincident

D
intersecting at (b, a)

Solution

The pair of equations x = a and y = b graphically represents lines which are intersecting at (a, b), as when we plot the graphs x=a will run parallel to y-axis and y=b will run parallel to x-axis but they will intersect each other at point (a,b)
Question 3
1 / -0

The number of solutions of two linear equations representing intersecting lines is/are

A
1

B
2

C
∞

D
0

Solution

The number of solutions of two linear equations representing intersecting lines is 1 because two linear equations representing intersecting lines has a unique solution.
Question 4
1 / -0

The number of solutions for two linear equations representing parallel lines is/are

A
1

B
∞

C
0

D
2

Solution

The number of solutions of two linear equations representing parallel lines is 0 because two linear equations representing parallel lines has no solution and they are inconsistent.
Question 5
1 / -0

The number of solutions of two linear equations representing coincident lines is/are

A
0

B
1

C
5

D
infinite solution

Solution

The number of solutions of two linear equations representing coincident lines are ∞ because two linear equations representing coincident lines has infinitely many solutions.