Question

Which of the following has the same solution as this system of equations? 4x+9y=102x+3y=12

Answer 1

System C

Step-by-step explanation

All of these options show systems where the first equation is the same as the first equation of the given system. Then, to find which one has the same solution, we have to find which one's second equation is equivalent to the second equation of the given system.

An equivalent equation is an equation whose coefficients and independent terms have been multiplied or divided by a constant. If we multiply the second equation of the given system by 2,

`\begin{gathered} 2(2x+3y=12) \\ \\ 2\cdot2x+2\cdot3y=2\cdot12 \\ \\ 4x+6y=24 \end{gathered}`

We got the second equation of the system of option C.

Hence, the system that has the same solution is system C.