Question

the system of equation 2x-5y= and 4x-10y-16=0 has
a unique
no solution
infinitely many
2 solutions

Answer 1

Answer:

a unique solution is the answer

Answer 2

Incorrect question.

Correct question:

The system of equation 2 x - 5 y = 8 and 4 x - 10 y - 16 = 0 has  

A unique

No solution

Infinitely many

Two solutions

Answer:

Infinitely many  solution.

Step-by-step explanation:

Given :

2 x - 5 y = 8

Rewrite as

2 x - 5 y - 8 = 0  ....( i )

4 x - 10 y - 16 = 0  ... ( ii )

From ( i ) and ( ii ) we get

$\large a_1=2 , \ b_1=-5 \ and \ c_1=-8\\\\\\\large a_2=4 , \ b_2=-10 \ and \ c_2=-16$

We can see

$\large \dfrac{2}{4} =\dfrac{-5}{-10}= \dfrac{-8}{-16} =\dfrac{1}{2}$

When ratio of all coefficient are equal then it has many solution.

We also know formula for many solution.

$\large \dfrac{a_1}{a_2} =\dfrac{b_1}{b_2}= \dfrac{c_1}{c_2}$

Since condition is satisfy it has infinitely many solution.