Question

Direction Answer the questions from 31-35 based on the following case. Mohit went for shopping in the evening by metro with his father who is an expert in mathematics. He told Mohit that path of metro A is given by the equation x + 2y = 4 and path of metro B is given by the equation x + 2y = 6. Help Mohit to solve the questions.​

Answer 1

Answer:

x=0

y=2

Step-by-step explanation:

x+2y=4 -(1) equation

x+2y=6 -(2) equation

multiply eq 1 with 3

multiply eq 2 with -2

3x+6y=12

-2x-6y=12

x=o sub x value in any equation

0+2y=4

y=2

y value in any equation

x+2(2)=4

x+4=4

x=4-4=0

x=0 y=2

Answer 2

Given: Mohit went for shopping in the evening by metro with his father who is an expert in mathematics. He told Mohit that path of metro A is given by the equation x + 2y = 4 and path of metro B is given by the equation x + 2y = 6.

To find: 1- Point of intersection of x+2y= 4 with the X axis and Y axis

2- Point of intersection of x+2y= 6 with the X axis and Y axis

3- Coordinates of intersection of the two given equations

Solution: Let equation (i) be x+2y= 4 and equation (ii) be x+2y= 6

For the intersection of x+2y = 4 with the X axis, put y= 0 in the equation since every y coordinate on X axis = 0.

x+ 2y =4

=> x + 2×0 = 4

=> x = 4

Therefore, coordinates of intersection with X axis is (4,0).

For the intersection of x+2y = 4 with the Y axis, put x= 0 in the equation since every x coordinate on Y axis = 0.

x+ 2y =4

=> 0 + 2y= 4

=> y = 2

Therefore, coordinates of intersection with Y axis is (0,2).

Therefore, the correct option is option (a) (4,0),(0,2)

For the intersection of x+2y = 6 with the X axis, put y= 0 in the equation since every y coordinate on X axis = 0.

x+ 2y =6

=> x + 2×0 = 4

=> x = 6

Therefore, coordinates of intersection with X axis is (6,0).

For the intersection of x+2y = 6 with the Y axis, put x= 0 in the equation since every x coordinate on Y axis = 0.

x+ 2y =6

=> 0 + 2y= 6

=> y = 3

Therefore, coordinates of intersection with Y axis is (0,3).

Therefore, the correct option is option (c) (6,0),(0,3)

Let x+2y-4=0 be ax+by+c= 0 and x+2y-6= 0 be px+qy+r= 0.

Here, a/p = 1/1= 1

b/q= 2/2 = 1

c/r = -4/-6= 2/3

Here, a/p = b/q which is not equal to c/r which is a necessary condition for no solution to a pair of linear equations.

Therefore, coordinates of point of intersection - option (d) does not exist.