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

Please explain how to solve so I can understand

Answer 2

ok I would use the elimination method (one method you can apply to all systems)

Answer 3

your goal is to eliminate x or y, your choice

Answer 4

4x and -12x
if you try to eliminate the x's you will need the same number
I will choose 12 because 4 times 3 is 12

Answer 5

I can create 12x by multiplying 3 to 4x

Answer 6

that is one choice,
if I choose to eliminate the y's

Answer 7

what number would I use?

Answer 8

-3y and 9y ...you could use 9

Answer 9

Try multiplying the first equation by -3. What do you get?

Answer 10

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

Multiply first equation by -3:
-12x + 9y = -18
Compare this to the second equation:
The left hand sides are identical. But the right hand side is not. This is impossible. There are no values of x and y that can make -12x + 9y be -18 AND -24 at the same time.

Therefore, this system of equations has no solution.

Answer 11

what did you mean by the left hand side being identical?

Answer 12

After multiply first equation by -3 I got: -12x + 9y = -18
Compare this to the second equation: -12x + 9y = -24
The left hand side in both equations is the same: -12x + 9y

How can the same thing (-12x+9y) be two different things: -18 AND -24?

So no solutions because the equations are incompatible.

Answer 13

Understood...thank you very much. ♥