Chapter 6.5, Problem 10PPS

To determine

To solve the given system of equations with the best method

Answer to Problem 10PPS

No Solution.

Explanation of Solution

Given:

Equations:

  $4x+y=3$

  $y=-4x-1\Rightarrow 4x+y=-1$

From the above equations, it can be observed that 4x + y is common in both the given equations which means that both the lines are parallel to each other with different y - intercepts which are 3 and -1.

Hence there will be no possible solution. It will be easy to observe this using graph.

So, in this case graphical method will be more convenient and best.

Calculation:

Let,

  $\begin{array}{l}4x+y=\mathrm{3.......}(i)\\ 4x+y=-\mathrm{1.......}(ii)\end{array}$

Calculation of graph:

Consider, $y=3-4x$

Values of x	Values of y
0	3
1	-1
2	-5
3	-9
4	-13

By taking different values of x, the graph can be plotted.

Graph:

  

Calculation of graph:

Consider, $y=-4x-1$

Values of x	Values of y
0	-1
1	-5
2	-9
3	-13
4	-17

By taking different values of x, the graph can be plotted.

Graph:

  

Plotting both the graphs on the same co-ordinate plane:

  

Interpretation:

From the above graph, it is clear that, there is no common point of intersection for these two graphs.

Hence, there is no possible solution.

Conclusion:

Therefore, there is no possible solution.