[size=150][math]\begin{cases} \begin {align}4x + 3y &= 10\\ \text-4x + 5y &= 6 \end{align} \end{cases}[/math][br][br]Here is his work: [br][table][tr][td][math]\begin {align}4x + 3y &= 10\\ \text-4x + 5y &= \hspace{2mm}6 \quad+\\ \overline {\quad 0 + 8y} &\overline{ \hspace{1mm}= 16 \qquad}\\ y &= 2 \end{align}[/math][/td][td][math]\begin {align}4x + 3(2) &= 10\\ 4x + 6 &= 10\\ 4x &= 4\\ x &= 1 \end{align}[/math][br][/td][/tr][/table][/size][br][size=150]Make sense of Diego’s work and discuss with a partner:[/size][br][list][*]What did Diego do to solve the system?[/*][*]Is the pair of [math]x[/math] and [math]y[/math] values that Diego found actually a solution to the system? How do you know?[/*][/list]

[size=150]Does Diego’s method work for solving these systems? Be prepared to explain or show your reasoning.[br][/size][math]\begin {cases} \begin {align}2x + y &= 4\\ x - y &= 11 \end {align} \end {cases}[/math][br]or[br][math]\begin {cases} \begin{align} 8x + 11y &= 37\\ 8x + \hspace{4.5mm} y &= \hspace{2mm} 7 \end{align} \end{cases}[/math]

[table][tr][td]System A[/td][td]System B[/td][td]System C[/td][/tr][tr][td][math]\begin {cases}\begin {align}4x + 3y &= 10\\ \text-4x + 5y &= \hspace{2mm}6 \end{align} \end{cases}[/math][br][/td][td][math]\begin {cases} \begin {align}2x + y &= 4\\ x - y &= 11 \end {align} \end {cases}[/math][/td][td][math]\begin {cases} \begin{align} 8x + 11y &= 37\\ 8x + \hspace{4mm} y &= \hspace{2mm} 7 \end{align} \end{cases}[/math][/td][/tr][/table][size=150]For each system:[br][/size][list][*]Use graphing technology to graph the original two equations in the system. Then, identify the coordinates of the solution.[/*][*]Solve the system of equations by elimination and check your solution.[/*][/list]