Chapter 6.1, Problem 41PPE

(a)

To determine

To analyse: The system having $g\ge h$ has exactly one solution.

Answer to Problem 41PPE

The solution is sometimes.

Explanation of Solution

Given information:

Consider the system at the right.

y = gx + 3

y = hx + 7

Formula used:

The lines will not intersect each other

Calculation:

Consider the Statement given in the question:

If $g>h$ the lines intersect at one point but $g=h$ then the lines will not intersect each other

Hence, for $g\ge h$ sometimes the line will intersect.

Thus, the solution is sometimes.

Conclusion:

The solution is sometimes.

(b)

To determine

To analyse: The system having $g\le h$ has exactly one solution.

Answer to Problem 41PPE

The solution is sometimes.

Explanation of Solution

Given information:

Consider the system at the right.

y = gx + 3

y = hx + 7

Formula used:

The lines will not intersect each other

Calculation:

Consider the Statement given in the question:

If $g<h$ the lines intersect at one point but $g=h$ then the lines will not intersect each other

Hence, for $g\le h$ sometimes the line will intersect.

Thus, the solution is sometimes.

Conclusion:

The solution is sometimes.