Question

Solve by substitution. 3x+6y=21 -8x+y=63
What is the solution?

Answer 1

The solution is y=7, x=-7


lsolate x for 3x+6y=21; x=7-2y

Substitute x=7-2y

[-8(7-2y)+y=63]

lsolate y for -8(7-2y)+y=63: Y=7
For x=7-2y
Substitute y=7
X=7-2 time 7
X=-7

Solution is y=7, x=-7

Answer 2

`\bf \begin{cases} 3x+6y=21\\ \cline{1-1} -8x+y=63\\ \boxed{y}=63+8x \end{cases}~\hspace{7em}\stackrel{\textit{substituting on the 1st equation}}{3x+6\left( \boxed{63+8x} \right)}=21`

`\bf 3x+378+48x=21\implies 51x+378=21\implies 51x=-357 \\\\\\ x=\cfrac{-357}{51}\implies \blacktriangleright x=-7 \blacktriangleleft \\\\\\ \stackrel{\textit{since we know that}}{y=63+8x\implies }y=63+8(-7)\implies y=63-56\implies \blacktriangleright y=7 \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill (-7,7)~\hfill`