Lesson 1: Introduction to Systems and Solving by Graphing — Practice Questions

1. 1. Which ordered pair is a solution to the system of equations $$\begin{cases} x - 2y = 6 \\ 3x + y = 4 \end{cases}$$?

   • A. (4, -1)
   • B. (0, -3)
   • C. (2, -2)
   • D. (1, 1)

2. 2. The ordered pair $(3, b)$ is a solution to the system of equations $$\begin{cases} x + y = 5 \\ 2x - y = 4 \end{cases}$$. What is the value of $b$? ___

3. 3. Is the ordered pair $(4, -1)$ a solution to the system of equations $$\begin{cases} 2x + y = 7 \\ x - y = -1 \end{cases}$$?

   • A. No, because it does not satisfy the second equation.
   • B. No, because it does not satisfy the first equation.
   • C. Yes, because it satisfies the first equation.
   • D. Yes, because it satisfies both equations.

4. 4. The ordered pair $(1, 5)$ is tested as a solution for the system $$\begin{cases} y = 3x + 2 \\ y = -2x + 7 \end{cases}$$. It satisfies the first equation. When substituted into the second equation, $y$ evaluates to ___.

5. 5. Why is the ordered pair $(1, 1)$ not a solution to the system of equations $$\begin{cases} 4x - y = 3 \\ x + y = 1 \end{cases}$$?

   • A. It does not satisfy the equation $4x - y = 3$.
   • B. It does not satisfy the equation $x + y = 1$.
   • C. It does not satisfy either equation.
   • D. A solution must contain a zero.

6. 6. When solving a system of linear equations by graphing, what does the point of intersection of the two lines represent?

   • A. The solution to the system
   • B. A point on only one of the lines
   • C. The y-intercept of one line
   • D. The x-intercept of one line

7. 7. By graphing the system of equations $\begin{cases} y = x + 1 \\ y = -x + 5 \end{cases}$, you find the solution point $(x, y)$. What is the x-coordinate of this solution? ___

8. 8. The solution to the system of equations $\begin{cases} x + y = 8 \\ 2x - y = 4 \end{cases}$ is the point $(x, y)$. What is the value of $y$? ___

9. 9. Which ordered pair is the solution to the system of equations $\begin{cases} y = 2x - 1 \\ y = -x + 8 \end{cases}$?

   • A. (3, 5)
   • B. (2, 6)
   • C. (5, 3)
   • D. (1, 1)

10. 10. Consider the system of equations $\begin{cases} x = 3 \\ x + y = 7 \end{cases}$. The solution is the point $(3, y)$. Find the value of $y$. ___