Question

Two systems of equations are given below.
For each system, choose the best description of its solution.
If applicable, give the solution.
System A
4x+5y=5
4x+ 5y=6
The system has no solution.
• The system has a unique solution:
(x, y) = CD
• The system has infinitely many solutions.
System B
y=9x
y =2x
•
) The system has no solution.
• ) The system has a unique solution:
(x, y) = CD
• The system has infinitely many solutions.

Answer 1

System A:
Subtract the two equations: (4x+5y)-(4x+5y)=5-6 ⇒ 0 = −1, impossible.
So the system has no solution.

System B:
Set 9x = 2x ⇒ 7x = 0 ⇒ x = 0, hence y = 0.
So the system has a unique solution: (x,y) = (0,0).