MathAdmin: Created page with "''' Question ''' Solve the following system of equations
:: $\begin{align} 2x + 3y &= & 1\\ -x + y & = & -3\end{align}$ {| class="mw-collapsible mw-collapse..."

2015-06-01T01:23:01Z

Created page with "''' Question ''' Solve the following system of equations <br> ::<math> \begin{align} 2x + 3y &= & 1\\ -x + y & = & -3\end{align}</math> {| class="mw-collapsible mw-collapse..."

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''' Question ''' Solve the following system of equations <br>
::<math> \begin{align} 2x + 3y &= & 1\\ -x + y & = & -3\end{align}</math>

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
!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.
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 1:
|-
|Add two times the second equation to the first equation. So we are adding <math>-2x + 2y = -6</math> to the first equation.
|-
|This leads to:
|-
|
::<math>\begin{array}{rcl}
0 + 5y &=& -5\\
-x + y &=& -3
\end{array}</math>
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Step 2:
|-
|This gives us that <math>y = -1.</math>
|-
|Now we just need to find x. So we plug in -1 for y in the second equation.
|-
|
<math>\begin{array}{rcl}
-x -1 &=& -3\\
-x & =& -2\\
x&=&2
\end{array}</math>
|}

{| class="mw-collapsible mw-collapsed" style = "text-align:left;"
! Final Answer:
|-
|<math>x = 2,~ y = -1</math>
|}

[[005 Sample Final A|'''<u>Return to Sample Exam </u>''']]

005 Sample Final A, Question 9 - Revision history

MathAdmin: Created page with "''' Question ''' Solve the following system of equations :: \begin{align} 2x + 3y &= & 1\\ -x + y & = & -3\end{align} {| class="mw-collapsible mw-collapse..."

MathAdmin: Created page with "''' Question ''' Solve the following system of equations
:: $\begin{align} 2x + 3y &= & 1\\ -x + y & = & -3\end{align}$ {| class="mw-collapsible mw-collapse..."