005 Sample Final A, Question 9
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Question Solve the following system of equations
| Foundations: |
|---|
| 1) What are the two methods for solving a system of equations? |
| 2) How do we use the substitution method? |
| 3) How do we use the elimination method? |
| Answer: |
| 1) The two methods are the substitution and elimination methods. |
| 2) Solve for x or y in one of the equations and substitute that value into the other equation. |
| 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. |
| Step 1: |
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| Add two times the second equation to the first equation. So we are adding Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle -2x + 2y = -6} to the first equation. |
| This leads to: |
|
| Step 2: |
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| This gives us that Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle y = -1.} |
| Now we just need to find x. So we plug in -1 for y in the second equation. |
|
Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \begin{array}{rcl} -x -1 &=& -3\\ -x & =& -2\\ x&=&2 \end{array}} |
| Final Answer: |
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| Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle x = 2,~ y = -1} |