Question Solve the following system of equations
| Foundations:
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| 1) What are the two methods for solving a system of equations?
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| 2) How do we use the substitution method?
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| 3) How do we use the elimination method?
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| Answer:
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| 1) The two methods are the substitution and elimination methods.
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| 2) Solve for x or y in one of the equations and substitute that value into the other equation.
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| 3) Multiply one equation by some number on both sides to make one of the variables, x or y, have the same coefficient and add the equations together.
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| Step 1:
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| Add two times the second equation to the first equation. So we are adding Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle -2x+2y=-6}
to the first equation.
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| This leads to:
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| Step 2:
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| This gives us that Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle y=-1.}
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| Now we just need to find x. So we plug in -1 for y in the second equation.
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Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle {\begin{array}{rcl}-x-1&=&-3\\-x&=&-2\\x&=&2\end{array}}}
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| Final Answer:
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| Failed to parse (Conversion error. Server ("https://wikimedia.org/api/rest_") reported: "Cannot get mml. Server problem."): {\displaystyle x=2,~y=-1}
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