Question

Answer two questions about Systems A and B:System A: 8x - 3y = 0 2x + 7y = 3System B: 8x – 3y = 08x + 28y = 121) How can we get System B from System A?2) Based on the Previous answer are the systems equivalent? In other words do they have the same solution?

Answer 1

Answer

1) Option A is correct.

One of the equations is replaced by a multiple of itself.

2) The two systems have the same solutions.

Explanation

1) System A

8x - 3y = 0

2x + 7y = 3

System B

8x - 3y = 0

8x + 28y = 12

We can see that the two equations have the same first equations, but careful observation of the second equations show that the second equation of system B is simply 4 multiplied by the second equation of system A.

So, one of the equations is replaced by a multiple of itself.

2) From either solving this or simple mathematics knowledge of first reducing the second equations to the same form (by dividing through the second equation of system B by 4), we would end up with the two equations having the same equations.

And hence, the two systems will have the same solutions too.

Hope this Helps!!!