The system of equations which has the same solution as the system Mr. Nigma is solving are 4x-3y=9, -15y=-1 and 2x+6y=5, 10x=23.
What is a system of equation?
A system of equation is the set of equation in which the finite set of equation is present for which the common solution is sought.
Mr.Nigma is solving the system of equations. The first equation in this system is,
[tex]4x-3y = 9\\-3y=9-4x\\3y=-9+4x\\y=\dfrac{-9+4x}{3}[/tex] ....1
The second equation in this system is,
[tex]2x+6y=5[/tex]
Put the value of y from equation 1 in this equation,
[tex]2x+6(\dfrac{-9+4x}{3})=5\\2x-18+8x=15\\10x=5+18\\10x=23[/tex]
Thus, the option D is correct. Now take the second equation as,
[tex]2x+6y=5\\2x=5-6y\\x=\dfrac{5-6y}{2}[/tex]
Put this value in first equation as,
[tex]4(\dfrac{5-6y}{2})-3y=9\\10-12y-3y=9\\-15y=9-10\\-15y=-1[/tex]
Thus, the option 1 is also correct.
Hence, the system of equations which has the same solution as the system Mr. Nigma is solving are 4x-3y=9, -15y=-1 and 2x+6y=5, 10x=23.
Learn more about the system of equations here;
https://brainly.com/question/13729904
