Question

How many solutions exist for the system, x + y = 1 and y = -x + 1?


A. no solution
B. one solution
C. infinitely many solutions

Answer 1

Notice that the two equations are identical because
y = -x + 1
<=> y + x = x - x + 1
= 1

Hence you only have one equation

x + y =1.

How many solutions are there to that equation?

Answer 2

1?

Answer 3

Well,
x =1, y = 0
is one solution

x = 2, y = -1
is another solution

So is
x = 0, y =1

In fact, if you drew the graph of that equation, there would be an infinite number of points on it, reflecting the fact there are an infinite number of answers.

Answer 4

ok thanks :)

Answer 5

In general, if you have two variables you need two equations to have a unique solution.

With two variables and one equation, there are an infinite number of solutions.