true or false

Question

 A system comprising two linear equations in two variables has a unique solution if and only if the straight lines represented by the equations are nonparallel.  True or False

 

If you think the statement is true, then show that it is true. On the other hand, if you think the statement is false, then give an example that disproves the statement.

Answer 1

true

nonparallel lines intersect in one point

y=x+4

y=2x+6

subtract

0=x+2

x=-2, y=2

Also keep in mind that you can have one line directly on top of another line which means that there are infinitely many solutions.

y=x+4

3y=3x+12 for example