Question

Without solving the systems, explain why the following systems must have the same solution.

System (a): 4x-5y=13 System (b): 8x-10y=26
3x+6y=11 x-11y=2

Answer 1

if the system has the same solution, that means that there's an intersection

Answer 2

The equations are identities of each other. Note that the first equation of system (b) is simply the first equation of system (a) multiplied by 2.
Further note: That the 2nd equation of system (b) the 2nd equation of system (a) subtracted from system (a) first equation. In other words, system is really system a information.

Answer 3

hey!! it applies the concept of your previous question, part 2) it says: if (a,b) is solution of (P=0 and Q+kP =0) then, (a,b) is solution of (P=0 and Q=0)

Answer 4

then (a,b) is a solution of Q and P