Question

Identify a possible first step using the elimination method to solve the system and then find the solution to the system.

2x - 5y = 11
3x + 2y = 7
Multiply first equation by 3 and second equation by 2. solution (5, 1)
Multiply first equation by 2 and second equation by - 3 solution (3-1)
Multiply first equation by -3 and second equation by-2. solution (3.1).
Multiply first equation by -3 and second equation by 2. solution (3,-1) |

Answer 1

`\bf \begin{array}{lcrrrrr} 2x-5y=11&\stackrel{\stackrel{\textit{\large first step}}{\downarrow }}{* -3}\implies &-6x&+&15y&=&-33\\ 3x+2y=7&* 2\implies &6x&+&4y&=&14\\\cline{3-7} &&0&+&19y&=&-19 \end{array} \\\\\\ y = \cfrac{-19}{19}\implies \boxed{y=-1} \\\\\\ \stackrel{\textit{substituting on the 1st equation}}{2x-5(-1)=11\implies 2x+5=11}\implies 2x=6\implies x = \cfrac{6}{2}\implies \boxed{x = 3} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill (3~~,~~-1)~\hfill`