Answer:
The correct answers are 1) ( -4,-2 ); 2) Infinite solution; 3) ( 1,-2 ); 4) No solution; 5) ( 0,5 ); 6) ( [tex]\frac{6}{5} , \frac{-9}{5}[/tex]).
Step-by-step 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 = [tex]\frac{6}{5}[/tex]
⇒ y = [tex]\frac{-9}{5}[/tex]
