Question

21. The pair of linear equations 7x - 3y = 4 and 14x + 4y = 5
have
a) ne solution (b) two solutions
c)many solutions (d) no solution​

Answer 1

Answer:

b) two solutions

hope this will help you

Answer 2

Answer:

The pair of linear equations 7x - 3y = 4 and 14x + 4y = 5

have (a) one solution

Step-by-step explanation:

7x - 3y = 4 .........................................(i)

14x + 4y = 5..........................................(ii)

• Comparing these with pair of equations of the form $a_{1}$x+$b_{1}$y+$c_{1}$ =0

      and $a_{2}$x+$b_{2}$y+$c_{2}$ =0,  we can write:

• $a_{1}$ = 7 , $b_{1}$ = -3 , $c_{1}$ = -4

         $a_{2}$ = 14 , $b_{2}$ = 4 , $c_{2}$ = -5

• so, $a_{1}$/$a_{2}$ = 7/14 = 1/2

        $b_{1}$/$b_{2}$ = -3/4    and    $c_{1}$/$c_{2}$ = 4/5

  ∵ $a_{1}$/$a_{2}$ ≠ $b_{1}$/$b_{2}$, so , the two given equations have a unique solution.

• For any pair of linear equation

       a₁ x + b₁ y + c₁ = 0

       a₂ x + b₂ y + c₂ = 0

a) a₁/a₂ ≠ b₁/b₂ (Intersecting Lines) .... Hence they have a unique Solution.

b) a₁/a₂ = b₁/b₂ = c₁/c₂ (Coincident Lines).... They have many Solution.

c) a₁/a₂ = b₁/b₂ ≠ c₁/c₂ (Parallel Lines)........ They don't have any solution.