Loading...

Section 5.2: Solving Systems of Linear Equations by Substitution — Practice Questions

  1. 1. Given the system of equations $y = 3x - 2$ and $2x + y = 13$, what is the value of $x$? The value of $x$ is ___.

  2. 2. To solve the system $3a + 4b = 20$ and $a - 2b = 0$ by substitution, what is the most efficient first step?

    • A. Solve the second equation for $a$.
    • B. Solve the first equation for $a$.
    • C. Solve the second equation for $b$.
    • D. Add the two equations together.
  3. 3. Solve the system of equations: $x + 2y = 10$ and $x - y = 1$. What is the value of $y$? The value of $y$ is ___.

  4. 4. Consider the system $3x + 2y = 10$ and $x - y = 1$. Using the substitution method, what is the value of $y$? The value of $y$ is ___.

  5. 5. What is the solution $(x, y)$ to the system of equations $x = 4y - 1$ and $2x + 3y = 13$?

    • A. (3, 1)
    • B. (1, 3)
    • C. (7, 2)
    • D. (-5, -1)
  6. 6. For which system of equations is substitution most efficient because one equation is already solved for a variable?

    • A. $\begin{cases} y = 2x + 1 \\ 3x + 4y = 12 \end{cases}$
    • B. $\begin{cases} x - 2y = 5 \\ 3x + y = 8 \end{cases}$
    • C. $\begin{cases} 2x + 3y = 7 \\ 5x - 4y = 6 \end{cases}$
    • D. $\begin{cases} 4x - y = 9 \\ 2x + 3y = 1 \end{cases}$
  7. 7. In which system is substitution efficient because a variable has a coefficient of 1 or -1, making it easy to isolate?

    • A. $\begin{cases} 2x + 5y = 10 \\ 3x - 4y = 8 \end{cases}$
    • B. $\begin{cases} 4x + 2y = 1 \\ 2x + 6y = 7 \end{cases}$
    • C. $\begin{cases} 5x - 2y = 3 \\ 2x + 3y = 11 \end{cases}$
    • D. $\begin{cases} x + 6y = 15 \\ 4x - 3y = 5 \end{cases}$
  8. 8. To solve the system $\begin{cases} 4x - y = 11 \\ 2x + 3y = 5 \end{cases}$ using substitution, you can first isolate $y$ in the first equation. What is $y$ in terms of $x$? $y = $ ___

  9. 9. True or False: For the system $\begin{cases} 5x + 2y = 9 \\ 3x - 4y = 1 \end{cases}$, substitution is the most efficient method to use.

    • A. True
    • B. False
  10. 10. Consider the system $\begin{cases} x + 8y = 10 \\ 3x - 5y = 14 \end{cases}$. To use substitution, you can solve the first equation for $x$. What is $x$ in terms of $y$? $x = $ ___