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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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21 votes
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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

User Anjum Sayed
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2 Answers

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10 votes


\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.

User Singmotor
by
3.2k points
10 votes
10 votes
Here is the work, the answer is no sol
Solve using the method of elimination , determine if the system has 1 solution, no-example-1
User Kevin Pope
by
2.7k points
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