In each of the following systems of equations determine whether the sy

1.	In each of the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:2x + y = 54x + 2y = 10
Answer» a₁x + b₁y + c₁ = 0 a₂x + b₂x + c₂ = 0 If \(\frac{a_1}{a_2}\) = \(\frac{b_1}{b_2}\) = \(\frac{c_1}{c_2}\) infinite solution , If \(\frac{a_1}{a_2}\) = \(\frac{b_1}{b_2}\) ≠ \(\frac{c_1}{c_2}\) no solution If \(\frac{a_1}{a_2}\) ≠ \(\frac{b_1}{b_2}\) ≠ \(\frac{c_1}{c_2}\) unique solution 2x + y = 5 4x + 2y = 10 Thus, \(\frac{1}{2}\) = \(\frac{1}{2}\) = \(\frac{1}{2}\) Infinitely many solution

In each of the following systems of equations determine whether the system has a unique solution, no solution or infinitely many solutions. In case there is a unique solution, find it:2x + y = 54x + 2y = 10

Answer»

a₁x + b₁y + c₁ = 0

a₂x + b₂x + c₂ = 0

If \(\frac{a_1}{a_2}\) = \(\frac{b_1}{b_2}\) = \(\frac{c_1}{c_2}\) infinite solution ,

If \(\frac{a_1}{a_2}\) = \(\frac{b_1}{b_2}\) ≠ \(\frac{c_1}{c_2}\) no solution

If \(\frac{a_1}{a_2}\) ≠ \(\frac{b_1}{b_2}\) ≠ \(\frac{c_1}{c_2}\) unique solution

2x + y = 5

4x + 2y = 10

Thus,

\(\frac{1}{2}\) = \(\frac{1}{2}\) = \(\frac{1}{2}\)

Infinitely many solution