2.3.4 Solving More Equations

Algebra 12.3.4 Solving More Equations

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Cool Down

Solve this system of equations without graphing. Be prepared to show your reasoning. Use this system of equations to answer questions 1 – 3.

${\begin{matrix} 5 x + y = 7 \\ y = - 20 x + 2 \end{matrix}$

What is the $x$ value?

Compare your answer:

$\frac{1}{5}$

What is the $y$ value?

Explain your solutions.

Compare your answer:

Your answer may vary, but here are some samples.

Substituting $20 x + 2$ for $y$ in the first equation, $5 x + y = 7$ , gives $5 x + (20 x + 2) = 7$ or $25 x + 2 = 7$ , which then gives $x = \frac{1}{5}$ . Substituting $\frac{1}{5}$ for $x$ in the first equation and solving for $y$ gives $y = 6$ .
The first equation, $5 x + y = 7$ , can be rearranged to $y = 7 - 5 x$ . Substituting $7 - 5 x$ for $y$ in the second equation gives $20 x + 2 = 7 - 5 x$ . Solving this equation leads to $x = \frac{1}{5}$ , and substituting $\frac{1}{5}$ for $x$ in either equation gives $y = 6$ .

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