Question

2x+3y-5=0 and x+y-z=0 this pair of equations represent ______ lines

a. Intersecting
b. Coincident
c. Parallel

With method please.. ​

Answer 1

Answer :

a. Intersecting

Note:

★ A linear equation in two variables represent a straight line .

★ The word consistent is used for the system of equations which consists any solution .

★ The word inconsistent is used for the system of equations which doesn't consists any solution .

★ Solution of a system of equations : It refers to the possibile values of the variable which satisfy all the equations in the given system .

★ A pair of linear equations are said to be consistent if their graph ( Straight line ) either intersect or coincide each other .

★ A pair of linear equations are said to be inconsistent if their graph ( Straight line ) are parallel .

★ If we consider equations of two straight line

ax + by + c = 0 and a'x + b'y + c' = 0 , then ;

• The lines are intersecting if a/a' ≠ b/b' .

→ In this case , unique solution is found .

• The lines are coincident if a/a' = b/b' = c/c' .

→ In this case , infinitely many solutions are found .

• The lines are parallel if a/a' = b/b' ≠ c/c' .

→ In this case , no solution is found .

Solution :

Here ,

The given pair of linear equations is ;

2x + 3y - 5 = 0 ------(1)

x + y - 2 = 0 -------(2)

Now ,

Comparing the equations (1) and (2) with the general linear equations ax + by + c = 0 and a'x + b'y + c' = 0 respectively , we have ;

a = 2

a' = 1

b = 3

b' = 1

c = -5

c' = -2

Now ,

a/a' = 2/1 = 2

b/b' = 3/1 = 3

c/c' = -5/-2 = 5/2

Clearly ,

a/a' ≠ b/b'

Hence ,

The given lines are intersecting .