Lesson 6-1: Solve Systems of Equations by Graphing — Practice Questions

1. 1. Is the ordered pair $(3, 8)$ a solution to the system of equations $y = 3x - 1$ and $y = x + 5$?

   • A. Yes, it satisfies both equations.
   • B. No, it only satisfies the first equation.
   • C. No, it only satisfies the second equation.
   • D. No, it satisfies neither equation.

2. 2. Which statement best describes the solution to a system of two linear equations?

   • A. An ordered pair that satisfies the first equation.
   • B. An ordered pair that satisfies the second equation.
   • C. An ordered pair that satisfies at least one of the equations.
   • D. An ordered pair that satisfies both equations simultaneously.

3. 3. The ordered pair $(-2, 1)$ is a solution to the system of equations $y = -2x - 3$ and $5x + Ay = -7$. What is the value of $A$? The value of $A$ is ___.

4. 4. Is the ordered pair $(4, -1)$ a solution to the system of equations $2x + y = 7$ and $x - y = -1$?

   • A. Yes, it is a solution.
   • B. No, it does not satisfy the second equation.
   • C. No, it does not satisfy the first equation.
   • D. No, it does not satisfy either equation.

5. 5. Consider the system $y = 4x + 6$ and $y = 9x - 19$. To check if $(5, 26)$ is a solution, you test the first equation: $4(5) + 6 = \_\_\_$.

6. 6. The sum of two numbers is 15 and their difference is 3. If a system of equations is graphed for this scenario, the intersection point gives the two numbers. The larger number is ___.

7. 7. A rectangle has a perimeter of 30 cm. Its length is twice its width. Which system of equations represents this situation, where $L$ is the length and $W$ is the width?

   • A. $2L + 2W = 30$ and $L = W + 2$
   • B. $L + W = 30$ and $L = 2W$
   • C. $2L + 2W = 30$ and $L = 2W$
   • D. $2L + 2W = 30$ and $W = 2L$

8. 8. A school sold 100 tickets for a concert. Adult tickets cost 10 dollars and child tickets cost 6 dollars, raising 760 dollars. The intersection of the graphed system is $(a, c)$. What is the value of $a$? $a$ = ___.

9. 9. When solving a real-world problem by graphing a system of two linear equations, what is the significance of the point where the two lines intersect?

   • A. A solution that works for only the first equation.
   • B. A solution that works for only the second equation.
   • C. The unique solution that satisfies both equations simultaneously.
   • D. The starting value for one of the quantities.

10. 10. One number is 5 more than another. The sum of the two numbers is 21. If this problem is modeled by a system of equations, the solution reveals the two numbers. The smaller number is ___.