Determining the Best Method for Solving a System of Equations

2.4.4 Determining the Best Method for Solving a System of Equations

2.4.4 • Determining the Best Method for Solving a System of Equations

Cool Down

Graphing technology should not be used in this cool down.

Use this linear equation to answer questions 1 – 2.

${\begin{matrix} 2 x + \frac{1}{2} y = 7 \\ 6 x - \frac{1}{2} y = 5 \end{matrix}$

Which would be a more helpful method for solving the system?

The answer is to add the two equations.

Explain or show how you know.

Compare your answer:

Your answer may vary, but here is a sample. $\frac{1}{2} y + - \frac{1}{2} y = 0$ , so adding the equations would eliminate the $y$ -variable and enable solving for $x$ .

Solve the system without graphing to answer questions 3 – 5.

Identify the $x$ coordinate of the solution.

Compare your answer:

$\frac{3}{2}$ or equivalent

Identify the $y$ coordinate of the solution.

Explain or show your reasoning.

Compare your answer:

Your answer may vary, but here is a sample.

$\begin{matrix} \underset{―}{2 x + \frac{1}{2} y = 7 + 6 x - \frac{1}{2} y = 5} \\ 8 x = 12 \\ x = \frac{12}{8} \\ x = \frac{3}{2} \end{matrix}$

Video: Determining the Best Method for Solving a System of Equations

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