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The values of x and y after solving equations

$3 x + y - 11 = 0; x - y - 1 = 0$

graphically are:

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x = 3 and y = 2

x = 3 and y = 4

x = 3 and y = 3

x = 3 and y = 1

answer is A.

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Detailed Solution

Given pair of linear equations:

3 x + y − 11 = 0 … 1 x − y − 1 = 0 … 2

To produce a graphical representation, create the appropriate table with at least two answers for each equation:
From equation (1),

y = 11 - 3 x

Then table for

3 x + y − 11 = 0

is,

x	$\frac{11}{3}$	0	3
$y = 3 x - 11$	0	11	2

So, points are

(\frac{11}{3} = 3.67, 0), (0, 11), and (3, 2)

.
From equation (2),

y = x - 1

Then table for

x - y - 1 = 0

is,

x	$1$	0	3
$y = x - 1$	0	-1	2

So, points are

1, 0

0, − 1

and

3, 2

.
Create a graph of both equations using the same scale of representation and the same graph paper:
On plotting points

(3.67, 0), (0, 11), (3, 2), (1, 0) and (0, - 1)

on the graph paper and joining them by a line, we get the following graph for the above equations.
Question Image

Discover the coordinates of the intersection of the two graphs.
In the graph, we observed that these two lines intersect at point C (3, 2).
Thus x = 3 and y = 2 is the solution of the given pair of equations.
Hence, option (1) is correct.

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