Question

Solve the system by the method of your choice. Identify systems with no solution and systems with infinitely many solutions, using set notation to express their solution sets.

4x - 3y = 6
-12x + 9y = -24

Answer 1

@ranga Help me Please

Answer 2

A. {( 3, 4)}
B. {(4/9 , -1/3})
C. {(x, y) | 4x - 3y = 6 }
D. ∅

Answer 3

Multiply the first equation by -3 and tell me what you get.

Answer 4

-12x - (-9y ) = 6

Answer 5

You have to multiply the right too. Also simplify -(-9y)

Answer 6

-12x + 9y = 18

Answer 7

close. you forgot the minus sign on the right (you are multiplying by -3)

-12x + 9y = -18

Compare this to the second equation and see if it makes any sense.

Answer 8

i am stuck over here.. how do i know if it makes sense? what do you mean by "if it makes sense"

Answer 9

compare:
-12x + 9y = -18 (modified first equation)
-12x + 9y = -24 (second equation)

The left hand sides are identical but the right hand sides are different!
Is it possible to find any x,y values that can make both equations true?
Definitely NOT. Whatever value you come up for x and y, if you put it into the two equations, the right hand side will be the same but the right hand side says they have to be -18 to satisfy the first and -24 to satisfy the second.

Therefore, there are NO solutions.

Answer 10

I mean the left hand side will be the same above.

Answer 11

so it means choice D is correct. Is it?

Answer 12

correct.

Answer 13

both the equations are same .. it will have infinitely many solutions

Answer 14

@nitish007 Both equations are NOT the same. They are inconsistent equations and therefore there are NO solution.

If you still think there are infinite solutions to these two equations then just give me one solution that satisfies both equations.