Mathematics, 26.06.2019 19:00 j015
Use the elimination method to solve the following system of equations. x+y=1 and x-y=-6 . the system has a single solution. the solution set is (x, y) (type an ordered pair, using integers or fractions.) b. there are infinitely many solutions. the solution set is (type an equation. type your answer in standard form.) c. the solution set is the empty set.
Answers: 1
![\bf \begin{array}{llll} x+y=1&\times(-1)\implies &\begin{matrix} -x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~-y&=-1\\ x-y=-6&&\begin{matrix} x \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~~~ -y&=-6\\ \cline{3-4}\\ &&~\hfill -2y&=-7 \end{array} \\\\\\ y=\cfrac{-7}{-2}\implies \blacktriangleright y=\cfrac{7}{2} \blacktriangleleft \\\\[-0.35em] ~\dotfill](/tpl/images/0020/4973/b12e8.png)
![\bf \stackrel{\textit{substituting on the 1st equation}}{x+\left( \cfrac{7}{2} \right)=1\implies x=1-\cfrac{7}{2}}\implies \blacktriangleright x=-\cfrac{5}{2} \blacktriangleleft \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \left(-\frac{5}{2}~~,~~\frac{7}{2} \right)~\hfill](/tpl/images/0020/4973/e0019.png)
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Use the elimination method to solve the following system of equations. x+y=1 and x-y=-6 . the system...
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