Lesson 2: Solving Systems by Substitution — Practice Questions

1. 1. Consider the system of equations: $y = 3x - 5$ and $2x + y = 10$. Using the substitution method, what is the value of $x$? ___

2. 2. Using the substitution method, what is the solution to the system of equations $x = 3y + 1$ and $2x + y = 9$?

   • A. $(4, 1)$
   • B. $(1, 4)$
   • C. $(7, 2)$
   • D. $(-2, -1)$

3. 3. Solve the system of equations $3x - y = 7$ and $2x + 3y = 1$. What is the value of $y$? ___

4. 4. Given the system $x + 2y = 6$ and $3x - 4y = 8$, which equation is a valid result of using the substitution method?

   • A. $3(6 - 2y) - 4y = 8$
   • B. $(6 - 2y) + 2y = 6$
   • C. $3x - 4(6 - x) = 8$
   • D. $x + 2(3x-8) = 6$

5. 5. Solve the system of equations $y = x + 1$ and $2x + 3y = 7$. What is the value of $x$? Express your answer as a fraction. ___