Method.........

Question

Select all systems that are equivalent to this system:

{6d+4.5e=16.5

{5d+0.5e=4

A {6d+4.5e=16.5

{45d+4.5e=4

B{30d+22.5e=82.5

{5d+0.5e=4

C{30d+22.5e=82.5

{30d+ 3e=24

D{6d+4.5e=16.5

{6d+0.6e=4.8

E{12d+9e=33

{10d+0.5e=8

F {6d+4.5e=16.5

{10d+ e=8

Answer 1

Hi Mark! Systems are equivalent if they can be formed from some combination of the original equations. For example, the second equation is 5d + 0.5e = 4. If we multiply the entire equation by 2, we get 10d + 1e = 8. This is the second equation in Letter F, and the first equation is exactly the same as the original first equation. So F would be equivalent to the original system. In Letter E, the original first equation is multiplied by 2 to get the new first equation. BUT, the new second equation is not correct. So F would not be equivalent. You can use this strategy to decide whether the other systems are equivalent or not.