Solve using the method of elimination , determine if the system has 1 solution, no solutions, or infinite solutions -8x+2y=8 4x+8y= -4 Show all work

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asked Oct 28, 2023 21.6k views

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Ashis Biswas · Answer 1 · 2023-10-29T07:57:09+0000

$\stackrel{\textit{2nd equation }* 2}{\begin{array}{rrrrr} -8x&+&2y&=&8\\ 2(4x&+&8y)&=&2(-4) \end{array}}\qquad \implies \qquad \begin{array}{rrrrr} -8x&+&2y&=&8\\ 8x&+&16y&=&-8\\\cline{1-5} 0&+&18y&=&0 \end{array} \\\\\\ 18y=0\implies y=\cfrac{0}{18}\implies \boxed{y=0} \\\\\\ \stackrel{\textit{we know that}}{4x+8y=-4}\implies 4x+8(0)=-4\implies 4x=-4\implies x\cfrac{4}{-4}\implies \boxed{x=-1} \\\\[-0.35em] ~\dotfill\\\\ ~\hfill \stackrel{\textit{one solution}}{(-1~~,~~0)}~\hfill$

you'd want to often enough check their slopes first, if the slopes differ, they meet, if equal, they're parallel and either never meet or meet everywhere.

Solve using the method of elimination , determine if the system has 1 solution, no solutions, or infinite solutions -8x+2y=8 4x+8y= -4 Show all work

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