Question

Solve the following pair of equations graphically:

$\begin{array}{l} 2 x + y = 6 \\ x - 2 y = 8 \end{array}$

Accepted Answer

The given equations are

$2 x + y = 6$ ----- (i)

$x - 2 y = 8$ ----- (ii)

Some of the values of $x$ and $y$ , satisfying equation (i) are given in the following table.

$x$ $- 1$ $0$ $6$

$y$ $8$ $6$ $- 6$

Some of the values of $x$ and $y$ satisfying equation (ii) are given in the following table.

$x$ $- 6$ $0$ $8$

$y$ $- 7$ $- 4$ $0$

The points obtained from the first table namely $(- 1, 8), (0, 6)$ and $(6, - 6)$ are plotted in the Cartesian plane. Joining these points, we get the straight line $A B$ . This is the graph of the equation $2 x + y = 6$ .

Again, in the same Cartesian plane, and taking the same units, the points obtained from the second table, namely $(- 6, - 7), (0, - 4)$ and $(8, 0)$ are plotted. Joining these points, we get the straight line $C D$ . This is the graph of the equation $x - 2 y = 8$ .

It is seen from the graph that the two straight lines $A B$ and $C D$ intersect at the point $P (4, - 2)$ . This is a point common to both the straight lines $A B$ and $C D$ . Therefore, the coordinates of $P$ will satisfy both the equations (i) and (ii).
Hence, the solution of the given pair of equations is given by
$x = 4$ and $y = - 2$ .

Manipur Board Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 1: EXERCISE 4.1

Manipur Board Mathematics Solutions for Exercise - Manipur Board Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 1: EXERCISE 4.1

Questions from Manipur Board Solutions for Chapter: Pair of Linear Equations in Two Variables, Exercise 1: EXERCISE 4.1 with Hints & Solutions

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