Pair of Linear Equations in Two Variables Test

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Pair of Linear Equations in Two Variables Test - 1

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Question 1
1 / -0

Every linear equation in two variables has

A
no solution

B
an infinite number of solutions

C
two solutions

D
one solution

Solution

Explanation:

A linear equation in two variables is of the form, ax + by + c = 0,
where geometrically it does represent a straight line and every point on this graph is a solution for given linear equation.

As a line consists of infinite number of points,

A linear equation has infinite number of solutions.
Question 2
1 / -0

Ten students of class X took part in Mathematics quiz. The number of girls is 4 more than that of the boys. The algebraic representation of the above situation is

A
x = y - 12 and y = 6 + x

B
y = x + 4 and x = 10-y

C
none of these

D
x – y = 10 and x + y = 4

Solution

Explanation:

Let number of boys = x

Number of girls = y

Given that total number of student is 10 so that

x + y = 10

subtract y both side we get

x = 10 – y

Given that If the number of girls is 4 more than the number of boys

So that

y = x + 4
Question 3
1 / -0

A system of two linear equations in two variables is inconsistent, if their graphs

A
intersect only at a point

B
coincide

C
do not intersect at any point

D
cut the x – axis

Solution

Explanation:

A system of two linear equations in two variables is inconsistent, if their graphsdo not intersect at any point.
In this case, a pair of lines represented by the system are parallel to each other. so they do not intersect each other at any point.
the system is an inconsistent system of linear equations and the equations are independent.
Question 4
1 / -0

A system of two linear equations in two variables has no solution, if their graphs

A
coincide

B
do not intersect at any point

C
intersect only at a point

D
cut the x – axis

Solution

Explanation:

A system of two linear equations in two variables is inconsistent, if their graphsdo not intersect at any point.
In this case, a pair of lines represented by the system are parallel to each other. so they do not intersect each other at any point.
then there are no solutions that are true for both equations.
Question 5
1 / -0

A system of two linear equations in two variables has a unique solution, if their graphs

A
coincide

B
cut the x – axis

C
do not intersect at any point

D
intersect only at a point

Solution

Explanation:

Number of solutions of a system of two linear equations in two variables are equal to number of common points between the graphs of given linear equations.

If a system has unique solution then their graphs must intersect in only one point.
Question 6
1 / -0

A system of two linear equations in two variables has infinitely many solutions, if their graphs

A
cut the x – axis

B
intersect only at a point

C
coincide with each other.

D
do not intersect at any point

Solution

Explanation:

A system of two linear equations in two variables has infinitely many solutions, if their graphs coincide with each other and all the points in one line are common with the other line.
Question 7
1 / -0

A system of two linear equations in two variables is consistent, if their graphs

A
intersect only at a point or they coincide with each other

B
cut the x – axis

C
coincide

D
do not intersect at any point

Solution

Explanation:

A system of two linear equations in two variables is consistent, if their graphs intersect only at a point, because it has a unique solution or they may coincide with each other giving infinite solutions.
Question 8
1 / -0

A system of two linear equations in two variables is dependent consistent, if their graphs

A
coincide

B
cut the x – axis

C
do not intersect at any point

D
intersect only at a point

Solution

Explanation:

A system of two linear equations in two variables is dependent consistent, if their graphs coincide with each other i.e. they superimpose each other and all points in one line are also solution for the other line .
Question 9
1 / -0

The lines representing the pair of equations 5x – 4y + 8 = 0 and 7x + 6y – 9 = 0

A
are coincident

B
none of these

C
are parallel

D
intersect at a point

Solution

Explanation:

=a1/a2=5/7

=b1/b2=-4/6

Since a1/a2 ≠ b1/b2

∴ lines are intersecting at a point

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Pair of Linear Equations in Two Variables Test - 1

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Pair of Linear Equations in Two Variables Test - 1

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SHARING IS CARING

Question 1

no solution

an infinite number of solutions

two solutions

one solution

Solution

Question 2

x = y - 12 and y = 6 + x

y = x + 4 and x = 10-y

none of these

x – y = 10 and x + y = 4

Solution

Question 3

intersect only at a point

coincide

do not intersect at any point

cut the x – axis

Solution

Question 4

coincide

do not intersect at any point

intersect only at a point

cut the x – axis

Solution

Question 5

coincide

cut the x – axis

do not intersect at any point

intersect only at a point

Solution

Question 6

cut the x – axis

intersect only at a point

coincide with each other.

do not intersect at any point

Solution

Question 7

intersect only at a point or they coincide with each other

cut the x – axis

coincide

do not intersect at any point

Solution

Question 8

coincide

cut the x – axis

do not intersect at any point

intersect only at a point

Solution

Question 9

are coincident

none of these

are parallel

intersect at a point

Solution

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