Question

If you have a system of two equations with two unknowns, and the graphs of

the two equations are the same, the system must have.

A. 1 solution
B. No Solution
C.At Least 1 Solution
D. More Than 1 Solution

Answer 1

D. More Than 1 Solution

Explanation:

Let the system of equations be:

`a_1x+b_1y=c_1...(1)`

`a_2x+b_2y=c_2...(2)`

If the graph of equation (1) and (2) are the same, then the two graphs coincide with each other.

What that means is that; the two graphs intersects at infinitely many points.

Therefore the system must have infinitely many solutions.

In other words the system has more than one solution.

NB: At least one solution means exactly one solution and/or more than one solution. But lines that coincide cannot have exactly one solution.