005 Sample Final A, Question 9

Question Solve the following system of equations

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{align} 2x + 3y &= & 1\\ -x + y & = & -3\end{align}}

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:
Add two times the second equation to the first equation. So we are adding $-2x+2y=-6$ to the first equation.
This leads to:
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} 0 + 5y &=& -5\\ -x + y &=& -3 \end{array}}

Step 2:
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:
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}