Solving More Equations

2.3.4 Solving More Equations

2.3.4 • Solving More Equations

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 in the solution?

Compare your answer:

$\frac{1}{5}$

What is the $y$ value in the solution?

Explain how you determined your solution.

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 $y = 6$ .

Building Character: Growth Mindset

Illustration of a person in a lab coat on a ladder watering a brain with orange clouds and leaves, symbolizing nurturing growth and creativity; gears in the background suggest ideas or mental processes.

Having a growth mindset means believing you can improve your abilities. Compared to a fixed mindset, a growth mindset encourages you to embrace challenges, sustain effort, and try new strategies. Think about your current sense of having a growth mindset. Are the following statements true for you??

After I make a mistake, I always look for ways to learn from it.
I love challenges because they make me smarter.

Don’t worry if none of these statements are true for you. Developing this trait takes time. Your first step starts today!