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 with explanation:

It is given that, the two set of equations,

  Ax+By=C ,(1)

  D x + E y=F(2)

has the solution (2,-3).

→→Equation (1) - Equation (2)

(A-D)x + (B-E)y=C-F(3)

And, Second equation is,  D x + E y=F(4)

Equation (3) and (4), when solved , will produce the same solution, as given equation.

→→→Multiply equation (1), by 2 and it to equation (2)

2 A x +2 B y +D x + E y=2 C +F

(2 A +D)x+(2 B +E)y=2 C +F

And , other equation is,   D x + E y=F

Option (2),is different.Will not produce the Same Solution.

→→→→Multiply equation (2), by -3 and combining it, with the equation (1)

   Ax+By=C

  -3 D x -3 E y=-3 F

Produce the same solution, that original equation will,

→→→→Multiply equation (2), by -5 and subtracting it, from the equation,

(A-5 D) x + (B-5 E) y= C- 5 F

D x + E y=F

→→→→→Will Give the same solution, that original equation will.

Now, Coming to Option 5

A x +(B+E)y=C→ Ax + B y + E y =C→ C+E y =C→E y=0→y=0

(A+B)x+E y = C +F→A x +B x+E y=C→C - By+B x+E×0=C→B x=0→x=0

Used equation (1), to solve both the equations

Does not give, the solution set, (2, -3).

⇒≡Option , (1), (3) and (4) are system of equations with the same solution that Original equation has.

it would rotate about 180 degrees.