2 x 2 system of equation what is the solution ?

Question

6x - 6y = 72

-30x + 30y = -360

Answer 1

I) 6x - 6y = 72
II) -30x + 30y = -360
those two equations are linearly dipendent, that means that both are the same, and one have to be "killed"

so the solution of that sistem is
y = x - 12

all the points on that line are the solution of that sistem

Answer 2

6x - 6y = 72- - - - - - - - - -Equation 1
- 30x + 30y = - 360- - - - Equation 2
- - - - - - - - - - - - - -
Multiply equation 1 by 5

6x - 6y = 72

5(6x) - 5(6y) = 5(72)

30x - 30y = 360
- - - - - - - - - - - -

30x - 30y = 360
- 30x + 30y = - 360
- - - - - - - - - - - - - -

The equations cancell each other. No solution

- - - - - - - - -s-

Answer 3

6x - 6y = 72 ----------- (1)

- 30x + 30y = -360 ------------(2)

multiplying eqn (1) by 5 we get ,

30x - 30y = 360 ----------(3)



as eqn (2) and (3) are same this equation has infinity solutions for every values of x and y .

Answer 4

It's true that the system has infinitely many solutions, but not all real numbers. The solutions are all the points which lie on the line given by either equation. We can say that for each x, there exists a y such that both equations hold. But to say that the equations hold for all real numbers implies that they are satisfied by every pair of reals (x,y), and that isn't true.

Answer 5

These are identical equations. There is no finite solution.