The system Ax+By=C has the solution (2,-3) where Dx + Ey=FA,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 +FAnd , other equation is,   D x + E y=FOption (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 FProduce 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 FD 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=0Used equation (1), to solve both the equationsDoes not give, the solution set, (2, -3).⇒≡Option , (1), (3) and (4) are system of equations with the same solution that Original equation has.