Question

What are the answers to: 1) y = x/2 and y = x + 2 2) 4x - 6y = 12 and -2x + 3y = -6 3) 8x - 4y = 16 and -5x - 5y = 5 4) 2x + 3y = 10 and 4x + 6y = 12 5) y = -3x/2 + 5 and y = -2x/3 + 5 6) y = x - 3 and y = -4x + 3

Answer 1

The correct answers are 1) ( -4,-2 ); 2) Infinite solution; 3) ( 1,-2 ); 4) No solution; 5) ( 0,5 ); 6) (
`(6)/(5) , (-9)/(5)`).

Explanation:

1) y = x/2 and y = x + 2

⇒ x = 2x + 4

⇒ x = -4

⇒ y = -2

2) 4x - 6y = 12 and -2x + 3y = -6

If we multiply -2x + 3y = -6 by (- 2) we get both the equation of line as the same. Thus we get an infinite number of common points,i.e. infinite solution to the pair of line.

3) 8x - 4y = 16 and -5x - 5y = 5

⇒ 2x - 4y = 4 and -x - y = 1

Subtracting one equation from the other gives x = 1 and y = -2.

4) 2x + 3y = 10 and 4x + 6y = 12

There are no solution to the pair of lines as both the lines are parallel and they would never meet.

5) y = -3x/2 + 5 and y = -2x/3 + 5

⇒ 2y + 3x = 10 and 3y + 2x = 15

⇒ 6y + 9x = 30 and 6y + 4x = 30

Subtracting one from the other gives x = 0 and y = 5.

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

⇒ x -3 = -4x + 3

⇒ x =
`(6)/(5)`

⇒ y =
`(-9)/(5)`