Pair Of Linear Equations In Two Variables - Practice Test - 1 - Class 9 MCQ

Every linear equation in two variables hasan infinite number of solutions. e.g. 2x+2y=12 the following values can satisfy the above equation: x = 3,y = 3x = 2,y = 4x = 4,y = 2,etc.

If a pair of linear equation is consistent, then the lines will beintersecting or coincident.

ΔPOQ is formed by the given three lines.

Given:

Since the pair of given linear equations has infinitely many solutions,

Let the cost of one chair be Rs. x and the cost of 1 table be Rs. y.
According to question,
4x+3y=21004x+3y=2100…….(i)
5x+2y=17505x+2y=1750…….(ii)
Solving by elimination method, 

Let number of girls be xx and number of boys be y.y. According to question, x+y=10 ……….(i) And x=4+y ⇒ x−y = 4……….(ii)

The pair of equations x = a and y = b graphically represents lines which are intersecting at (a, b).

The triangle formed by the lines 2x+3y = 12 with co-ordinate axes is shaded.
The area of the shaded region, i.e., 2x+3y = 12

Therefore, the system of given equations has a unique solution.

Let my son’s present age x years and my present age be y years.
According to question,

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 number of solutions do two linear equations representing intersecting lines is 1 because two linear equations representing intersecting lines has a unique solution.

A system of linear equations is said to be consistent, if it hasat least one solution.

For non-zero solution 

A system of two linear equations in two variables has no solution, 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 number of solutions do two linear equations representing parallel lines is 0 because two linear equations representing parallel lines has no solution.

A system of linear equations is said to be inconsistent, if it has no solution.

A system of two linear equations in two variables has a unique solution, if their graphsintersect only at a point.

If a pair of linear equations is consistent the two lines represented by these equations definitely have a solution, this implies that either lines are intersecting or coincident.

If the system has unique solution, then 

Given: 3x – 5y = – 16 ……….(i)
And 2x + 5y = 31 ……….(ii)
Adding eq. (i) and (ii), we get 5x = 15 ⇒ x = 3
Putting the value of x in eq. (ii), we get
2 (3) + 5y = 31 ⇒ 5y = 31 – 6 
⇒ y = 5

Let the two digit number be 10x+y.
According to question,
x+y=9 ……….(i)
And 10+y+27 = 10y+x
⇒ 9x−9y = −27
⇒ x−y = −3 ……….(ii) 
On solving eq. (i) and (ii), we get 
x = 3,y = 6
Therefore, the two digit number is 10×3+6 = 36