Chapter 6.5, Problem 33PFA

To determine

To check if the given statements are true

Answer to Problem 33PFA

C, D, G

Explanation of Solution

Given:

Equations:

  $\begin{array}{l}x+y=10\\ y=5x\end{array}$

  

Concept used:

Graphical method:

Solve the given system of equations by substituting random values of x to find y. Plot the points in a graph.

Calculation:

Let us substitute random values for x in $x+y=10$

x	-1	0	1	2
y	11	10	9	8

Now substitute random values for x in $y=5x$

x	-1	0	1	2
y	-5	0	5	10

Substitute the point in a graph, two straight lines are obtained.

Graph:

  

In the above graph, the red line represents the equation $x+y=10$ and the blue line represents the equation $y=5x.$

Inference:

The intersecting point is at $(1.667,8.333)$ . Therefore, the solution of x is at 1.667 and the solution of y is at 8.33.

Conclusion:

Therefore, the correct statements are C, D and G.