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The values of x and y after solving equations

x -y +1=0; 4x +3y =24

graphically are:

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An Intiative by Sri Chaitanya

x = 3 and y = 4

x = 3 and y = 5

x = 3 and y = 6

x = 3 and y = 2

answer is A.

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Detailed Solution

Given pair of linear equations:

x − y + 1 = 0 … 1 4 x + 3 y = 24 or 4 x + 3 y − 24 = 0 … 2

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

y = x + 1

Then table for

x − y + 1 = 0

is,

So, points are

0, 1

− 1, 0

and

3, 4

.
From equation (2),

y = 4 x − 24 3

Then table for

4 x + 3 y − 24 = 0

is,

So, points are

0, 8

6, 0

and

3, 4

.
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 placing points

0, 1

− 1, 0

0, 8

6, 0

and

3, 4

on a graph paper, then connecting those points 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 (3, 4).
Therefore, x = 3 and y = 4 is the solution of the given pair of equations.
Hence, option (1) is correct.

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