Question

Two systems of equations are given below. For each system, choose the best description of its solution.

x - 5y = 5
-x + 5y = -5

a. The system has no solution.
b. The system has a unique solution:
(x,y) = _______
c. The system has infinitely many solutions. They must satisfy the following equation:
y = ________

Answer 1

Infinitely many solutions.

They must satisfy
`y = (1)/(5)(x - 5)`

Explanation:

Given

`x - 5y = 5`

`-x + 5y = -5`

Required

The best description

Add both equations

`x - x - 5y + 5y = 5 - 5`

`0+0 =0`

`0 = 0` ---- this means that the system has infinitely many solutions.

Make y the subject in:
`-x + 5y = -5`

Add x to both sides

`5y = x - 5`

Divide through by 5

`y = (1)/(5)(x - 5)`

Hence, they must satisfy:
`y = (1)/(5)(x - 5)`