Algebra Regents Exam: Question 33 Explained

This video provides a detailed explanation of question 33 from the January 2020 Algebra Common Core NYS Regents exam. The video aims to help students understand the concepts and strategies needed to solve this type of problem. It is a valuable resource for students preparing for the Algebra Regents exam.

Question 33

The question asks to find the solution to the system of equations:

$$\begin{cases}
2x + y = 5 \
x - 2y = 10
\end{cases}$$

The video explains that there are two main methods to solve a system of equations: substitution and elimination.

Solution Using Substitution

The video demonstrates how to solve the system using substitution. The first step is to solve one of the equations for one variable in terms of the other. In this case, the video chooses to solve the second equation for x:

$$x = 2y + 10$$

The next step is to substitute this expression for x into the first equation:

$$2(2y + 10) + y = 5$$

The video then simplifies and solves for y:

$$4y + 20 + y = 5$$

$$5y = -15$$

$$y = -3$$

Finally, the video substitutes this value of y back into the equation for x:

$$x = 2(-3) + 10$$

$$x = 4$$

Solution Using Elimination

The video also demonstrates how to solve the system using elimination. The first step is to multiply one or both equations by a constant so that the coefficients of one of the variables are opposites. In this case, the video multiplies the second equation by 2:

$$\begin{cases}
2x + y = 5 \
2x - 4y = 20
\end{cases}$$

The next step is to subtract the second equation from the first equation. This eliminates x and allows us to solve for y:

$$5y = -15$$

$$y = -3$$

Finally, the video substitutes this value of y back into either of the original equations to solve for x:

$$2x + (-3) = 5$$

$$2x = 8$$

$$x = 4$$

Conclusion

The video concludes by showing that both methods lead to the same solution: x = 4 and y = -3. The video encourages students to practice solving systems of equations using both substitution and elimination to develop their understanding of these important concepts.

Key Takeaways

• Systems of equations can be solved using substitution or elimination.
• Substitution involves solving one equation for one variable and substituting that expression into the other equation.
• Elimination involves multiplying one or both equations by a constant so that the coefficients of one of the variables are opposites, then subtracting the equations to eliminate that variable.
• Both methods lead to the same solution.

This video is a valuable resource for students preparing for the Algebra Regents exam. It provides a clear and concise explanation of how to solve systems of equations using both substitution and elimination.