Dori
Dec 8, 2020

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Answer:

No. of solutions = 0

★ 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 .

Here ,

The given linear equations are ;

3x - 4y = 5 → 3x - 4y - 5 = 0

6x - 8y - 10 = 0

Now ,

Comparing the given linear equations with the general equations ax + bx + c = 0 and ax' + by' + c' = 0 respectively , we have ;

a = 3

a' = 6

b = -4

b' = -8

c = -5

c' = -10

Now ,

a/a' = 3/6 = 1/2

b/b' = -4/-8 = 1/2

c/c' = -5/-10 = 1/2

Clearly ,

a/a' = b/b' = c/c'

Thus ,

The given pair of lines are parallel and hence there will be no solution .

288

Stephen

Dec 8, 2020

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