Section 5.1: Solving Systems of Linear Equations 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. Which of the following pairs of equations forms a system of linear equations?

   • A. $y = 4x + 50$ and $z = 2w + 60$
   • B. $y = 7x + 10$
   • C. $y = 5x + 100$ and $y = 8x + 70$
   • D. $y = x^2 + 5$ and $y = 3x + 1$

7. 7. A system of equations is given by $C = 25h + 80$ and $C = 30h + 60$. What pair of variables is used in this system?

   • A. $C$ and $h$
   • B. $C$ and $x$
   • C. $y$ and $h$
   • D. $x$ and $y$

8. 8. Two friends are saving money. Sarah's savings are modeled by $A = 10w + 50$. Ben's savings are modeled by $A = 15w + 25$. Together, these two equations form a ___ of linear equations.

9. 9. Is the following statement true or false? "A system of linear equations must consist of two equations that use different variables."

   • A. True
   • B. False