Question

the graph of 2x+3y=6 and 4x-3y=6 intersect in
(1)infinite no. of points
(2)no point
(3)four points
(4)one point
​

Answer 1

Answer:

The graph intesect at (4) one point.

Step-by-step explanation:

As per the data given in the question,

By comparing equations and subtracting:

2x+3y=6......(i)×2  =           4x+6y=12

4x-3y=6.......(ii)  =            -   4x-3y=6

                                            9y = 6

Therefore, y = 2/3 and x = 2

Since, there is only one value of x and y.

So, The graph intesect at (4) one point.

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Answer 2

Option (4)-One point is the correct answer.

Given:

2x+3y=6 and 4x-3y=6

To Find:

The intersection of given lines.

Solution:

2x+3y =6

Multiply both sides by 2

2( 2x+3y )=6*2

4x+6y=12 ----------------------(1)

4x-3y= 6 ------------------------(2)

Subtracting Equation (1) and (2)

4x+6y-4x+3y = 12-6

9y = 6

y=6/9

y=2/3

Substituting y value in equation (1)

4x + 6*(2/3) = 12

4x + 4 =12

4x=12-4

4x=8

x=8/4

x=2

∴ The given equation intersect at point (2, 2/3)

⇒ It has only one intersection point

Option (4)-One point is the correct answer.

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