The values of x and y after solving equations

2x +y =6; 2x – y = 2

graphically are:

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x = 1 and y = 3

x = 1 and y = 2

x = 2 and y = 2

x = 1 and y = 1

answer is C.

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Detailed Solution

Given pair of linear equations:
2x + y = 6 ........(1)
2x – y =2 ........(2)
To produce a graphical representation, create the appropriate table with at least two answers for each equation:
From equation (1),

y = 6 - 2 x

Then, table for

2 x + y = 6

is,

x	3	0	4
y = 2x-6	0	6	-2

So, points are (3,0), (0,6), and (4, -2).
From equation (2),

y = 2 x - 2

Then table for

2 x − y + 2 = 0

is,

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

So, points are (0, -2), (1,0), and (2,2).
Create a graph of both equations using the same scale of representation and the same graph paper:
We obtain the following graph for the aforementioned equations by placing the points, (3,0), (0,6), (4, -2), (0, -2), (1,0), and (2,2) on the graph paper, and connecting them with a line.
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 (2,2).
Thus x = 2 and y = 2 is the solution of the given pair of equations.
Hence, option (3) is correct.

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