MathematicsThe graphs of 2x+3y-6=0, 4x-3y-6=0, x=2 and y=23 intersect at

The graphs of $2 x + 3 y - 6 = 0, 4 x - 3 y - 6 = 0, x = 2$ and $y = \frac{2}{3}$ intersect at

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A
Four points
B
One point
C
No points
D
Infinite number of points

Solution:

Given equations are

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

and

y = \frac{2}{3}

.
Solving the given equations

2 x + 3 y - 6 = 0

and

4 x - 3 y - 6 = 0

we get,

x = 2

and

y = \frac{2}{3}

.
Hence from all the four given equations the value of

x

2

and

y

\frac{2}{3}

Therefore, the graphs of all the four lines intersect in one point which is

(2, \frac{2}{3})

.
Hence, the correct option is 2.

The graphs of $2 x + 3 y - 6 = 0, 4 x - 3 y - 6 = 0, x = 2$ and $y = \frac{2}{3}$ intersect at

Solution:

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