@zaasmi said in MTH603 Quiz 1 Solution and Discussion:

@zaasmi said in MTH603 Quiz 1 Solution and Discussion:

If there are three equations in two variables, then which of the following is true?

A system of equations in three variables involves two or more equations, each of … Plug in these values to each of the equations to see that the solution satisfies all … when graphing each equation in the system and then finding the intersection point of … A three dimensional box with three slanted planes crossing through it.

Explanation:

The simple answer is yes.

If you have two consistent equations and they are linearly independent, then you will have to assign arbitrary values to one of the variables. If you have two consistent equations and they are linearly dependent, then you will have to assign arbitrary values to two of the variables, both cases lead to an infinite number of solutions. If they inconsistent, then obviously there is no solution.

Graphically two consistent linearly independent equations will form 2 planes in

R

3

that intersect and all solutions will lie on the line of intersection leading to an infinite number of solutions.

Two consistent linearly dependent equations will just be a single line in

R

3

and all solutions will lie on this line, leading to an infinite number of solutions.

If the two equations are inconsistent then you will have 2 parallel lines in

R

3

, and no point of intersection, hence no solutions.