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.