Answér :

Consistent

Note:

★ A linear equation is 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 linear equations are ;

12x + 20y = 8

3x - 5y = 3

The given equations can be REWRITTEN as ;

12x + 20y - 8 = 0

3x - 5y - 3 = 0

Clearly , we have ;

a1 = 12

a2 = 3

b1 = 20

b2 = -5

c1 = -8

c2 = -3

Now ,

a1/a2 = 12/3 = 4

b1/b2 = 20/-5 = -4

c1/c2 = -8/-3 = 8/3

Clearly ,

a1/a2 ≠ b1/b2

Thus ,

The given equations has an unique solution .

Hence ,

The given equations are consistent .