Chapter 3.2, Problem 50HP

To determine

The method of solving a linear algebraically and graphically.

Explanation of Solution

Let, the linear equation is:

  $2x-4=6$

To solve algebraically:

We have,

  $\begin{array}{l}2x-4=6\\ \Rightarrow 2x=10\\ \Rightarrow x=\frac{10}{2}\\ \Rightarrow x=5\end{array}$

Hence, the solution is: $x=5$

To solve graphically:

We have,

  $2x-4=6$

Hence, in terms of graph we have to find out the intersection of $y=2x-4$ and $y=6$ .

The intersection of the two graphs will give the solution.

Now,

Calculation of graph:

Consider, $y=2x-4$

Values of x	Values of y
0	-4
1	-2
2	0
3	2
4	4

Using the above table the graph can be plotted.

Graph:

Calculation of graph:

Consider, $y=6$

Values of x	Values of y
0	6
1	6
2	6
3	6
4	6

Using the above table the graph can be plotted.

Graph:

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

Interpretation:

The both graphs intersect at $(5,6)$ as observed in the graph.

Conclusion:

Hence, the solution is $x=5$