The values of x and y after solving equations

x + 2y = 5; 2x -3y =- 4

graphically are:

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x = 1 and y = 2

x = -1 and y = 2

x = 1 and y = -2

x = 1 and y = 3

answer is A.

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Detailed Solution

Given pair of linear equations,

x + 2 y = 5 ​ ​ ​ or x + 2 y − 5 = 0 … 1 2 x - 3 y = - 4 or 2 x - 3 y + 4 = 0 … 2

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

y = 5 − x 2

Then table for

x + 2 y − 5 = 0

is,

So, points are

0, 52 = 2.5, 5, 0 and 1, 2

.
From equation (2),

y = 2 x + 4 3

Then table for

2 x − 3 y + 4 = 0

is,

So, points are

0, 43 = 1.3, − 2, 0 and 1, 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 given equations by drawing points

(0, 2.5), (5, 0), (1, 2), (0, 1.3), and (- 2, 0)

on graph paper and connecting them with a line.
Question Image

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

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