Chapter 4, Problem 1MCP

In Exercises 1-3, solve each system by graphing.

1. $\{{}_{2x\text{ - }y=4}^{3x+\text{ 2}y=6}$

To determine

To solve:

The given system by graphing.

Answer to Problem 1MCP

Solution:

The solution of the given system is $x=2,y=0$.

Explanation of Solution

Given:

   $\begin{array}{l}3x+2y=6\\ 2x-y=4\end{array}$

Calculation:

In order to solve a pair of linear equations graphically, we follow the following steps:

Step 1:

Firstly, we re-write equation (1) as $y=\frac{6-3x}{2}$.

Step 2:

We find the co-ordinates that satisfy the given equation by assigning the proper values to x.

   $\begin{array}{l}\text{We take }x=0\text{ and we get }y=3\hfill \\ \text{Similarly, When we }x=2,\text{ we get} \hfill \\ y=0andx=4,\text{ we get} \hfill \\ y=-3\hfill \end{array}$

In this way, we get three co-ordinates $\left(0,3\right),\left(2,0\right)\text{ and }\left(4,-3\right)$.

Step 3:- We now plot these co-ordinates on a graph paper taking the values of x on x -axis and the values of y on y -axis and therefore we get a straight line by joining these three co-ordinates.

Step 4 :- We repeat the above steps for equation (2) and get another three co-ordinates that are (0,-4), (1,-2) and (2, 0). After plotting these points, we get another straight line.

The intersection of these two lines is a solution of the given linear equations.

Hence, the points of equation (1) are:

x	0	2	4
y	3	0	-3

And, the points of equation (2) are:

x	0	1	2
y	-4	-2	0

Graph can be plotted as:

Conclusion:

After plotting these equations on a graph paper, we get an intersecting point i.e. (2, 0) and this is the solution of the given linear equations.