Question

True or False: A system of two linear equations containing two variables always has at least one solution.
True or False: A solution of a system of equations consists of values for the variables that are solutions of each equation of the system.

Answer 1

im not sure if i fully understand this. But two linear equations with two variables.
i.e y=x and y=x-1
these two do not have any intersections (solutions) meaning the first one is false
... that is what i take from it anyway, i may be wrong

Answer 2

As @Taplin44 points out, keeping in mind that two linear equations are just two equations for lines, just picture what would happen if those 2 lines happen to be parallel lines....?

As for the second one, I find the wording ambiguous:
"A solution of a system of equations consists of values for the variables that are solutions of \( \Large \text {each}\) equation of the system."

The word "each" sounds like it means one set of values for one equation, and another set for the other system, would be a solution?? If it said:

"A solution of a system of equations consists of values for the variables that are solutions of \( \Large \text {both equations}\) of the system."

.....then it would be less ambiguous, and clearly true.

Answer 3

Thank you both so much.