Question

If you get 4=4 when solving a system of equations algebraically, it means there is no solution

A.) always
B.) sometimes
C.) never

Explain

Answer 1

C) never

Explanation:

It means the system of equations is true for all values of the variables that satisfy one of the equations. The other equation is identical, so any values that satisfy the first equation will also satisfy the second equation.

There will be an infinite number of solutions. There will never be no solution.

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Example:

x + y = 4

-x -y +4 = 0

Adding the two equations gives ...

(x +y) +(-x -y +4) = (4) + (0)

4 = 4

The solutions to this system are all values of x and y such that x+y=4. There are an infinite number of such solutions.