Question

the system ax+by=c has the solution (2,-3), where dx+ey=f a, b, c, d, e, and f are non-zero real numbers. select all the systems of equations with the same solution

Answer 1

It is definitely A and D since the equation is dependent, the equation should be multiples of each other

Answer 2

Answer: The system of equations which has the same solution as the given system are,

(A-D)x+(B-E)y= C-F , Dx+Ey=F

And, (A-5D)x+(B-5E)y=C-5F, Dx+Ey=F

Explanation:

Since here, Given System is, Ax+By=C has the solution (2,-3)

Where, Dx+Ey= F

⇒ If (2,-3) is the solution of Ax+By=C

Then By the property of family of the solution,

⇒ (2,-3) must be the solution of (A-D)x+(B-E)y=C-F, (A-5D)x+(B-5E)y=C-5F.

But it is not the solution of equation, (2A+D)x+(2B+E)y=C+2F, Ax+(B+E)y=C

Therefore second and fifth options are not correct.

Also we can not go to the third option.

Thus, Only Option first and fourth are correct.