Question

8. The point of intersection between the lines 3x+ 4y = 7 and 4x -y = 3 lie in the (a) 1st quadrant (b) 2nd quadrant (c) 3rd quadrant (d) 4th quadrant ​

Answer 1

SOLUTION

TO CHOOSE THE CORRECT OPTION

The point of intersection between the lines 3x + 4y = 7 and 4x - y = 3 lie in the

(a) 1st quadrant

(b) 2nd quadrant

(c) 3rd quadrant

(d) 4th quadrant

CONCEPT TO BE IMPLEMENTED

We know that in two dimensional geometry the Cartesian plane is divided by coordinate axis in 4 quadrant

1. Quadrant I : Both the x - coordinates and y - coordinates are positive

2. Quadrant II : The x - coordinate is negative and the y - coordinate is positive

3. Quadrant III : Both the x - coordinates and y - coordinates are negative

4. Quadrant IV : The x - coordinate is positive and the y - coordinate is negative

EVALUATION

Here the given equations are

3x + 4y = 7 - - - - - - (1)

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

Multiplying both sides of Equation 2 by 4 we get

16x - 4y = 12 - - - - - - (3)

Equation 1 + Equation 3 gives

19x = 19

⇒ x = 1

From Equation 2 we get

( 4 × 1 ) - y = 3

⇒ 4 - y = 3

⇒ y = 1

Thus the point of intersection between the lines is (1,1)

Since Both the x - coordinates and y - coordinates are positive

So the point lies on 1st quadrant

FINAL ANSWER

Hence the correct option is (a) 1st quadrant

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