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Solve the following system of linear equations graphically.

$3 x + 2 y − 4 = 0 2 x − 3 y − 7 = 0$

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x=2 and y=-1

x=3 and y=-1

x=-2 and y=-1

x=2 and y=1

answer is A.

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Detailed Solution

Given equations are,

3 x + 2 y − 4 = 0

…………(1)

2 x − 3 y − 7 = 0

……………(2)
To get the values of x and y, solve equation (1).

3 x + 2 y = 4

3 x = 4 − 2 y

x = 4 − 2 y 3

…………….(3)
In the equation(3), enter y = 0.

x = 4 − 20 3

x = 43

Now enter y=1 into the equation (3)

x = 4 − 21 3

x = 4 − 2 3

x = 23

Now enter y= 3 into the equation (3)

x = 4 − 23 3

x = 4 − 6 3

x = − 2 3

x	$43$	$23$		$− 23$
y	0	1	3

To get the values of x and y, solve equation (2).

− 3 y = 7 − 2 x

3 y = 2 x − 7

y = 2 x − 7 3

……………..(4)
Enter x=0 into the equation (4).

y = 20 − 7 3

y = − 7 3

Now enter x= 4 into the equation (4).

y = 24 − 7 3

y = 8 − 7 3

y = 13

Now enter x= 5 into the equation (4).

y = 25 − 7 3

y = 10 − 7 3

y = 33

y = 1

x	0	4	5
y	$− 73$	$13$		1

Form the graph for given equations

3 x + 2 y − 4 = 0

and

2 x − 3 y − 7 = 0

with the above obtained x and y values.
Question Image

From the graph, the solution of the given equations is x=2 and y=-1.
The correct option is (1).

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