Question

Use the substitution method to solve the system of equations. Choose the

correct ordered pair.
x + 2y = 12
- x = -y-6
A. (7.1)
B. (9,3)
C. (6,0)
D. (8,2)

Answer 1

`\bf \begin{cases} x+2y=12\\ \cline{1-1} -x=-y-6\\ \boxed{x}=y+6 \end{cases}\qquad \qquad \stackrel{\textit{doing some substitution in the 1st equation}}{\boxed{y+6}+2y=12\implies 3y+6=12} \\\\\\ 3y=6\implies y=\cfrac{6}{3}\implies \blacktriangleright y=2 \blacktriangleleft \\\\\\ \stackrel{\textit{since we know that }}{x=y+6\implies }x=(2)+6\implies \blacktriangleright x=8 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (8,2)~\hfill`