Which statement best describes the solution to a system of two linear equations when graphed on the same coordinate plane?

The point satisfies only the first equation.

The point satisfies only the second equation.

The point is where the two lines intersect.

The point is the y-intercept of the steeper line.

A point $(c, d)$ is tested and found to be a solution to a system of two linear equations. What does this mean graphically?

The point $(c, d)$ is the y-intercept of both lines.

The point $(c, d)$ is where both lines cross the x-axis.

The point $(c, d)$ is the origin.

The point $(c, d)$ lies on the graph of both lines.

Solving Systems of Linear Equations by Graphing Practice — Grade 9 math

Lesson 55: Solving Systems of Linear Equations by Graphing — Practice Questions

1. Which statement best describes the solution to a system of two linear equations when graphed on the same coordinate plane?
- A. The point satisfies only the first equation.
- B. The point satisfies only the second equation.
- C. The point is where the two lines intersect.
- D. The point is the y-intercept of the steeper line.
2. The graphs of $y = 2x - 1$ and $y = -x + 8$ intersect at a single point. If the x-coordinate of this point is 3, what is its y-coordinate? ___
3. Which ordered pair is the solution to the system of equations defined by $y = 3x - 2$ and $y = x + 4$?
- A. (2, 6)
- B. (1, 5)
- C. (4, 8)
- D. (3, 7)
4. The point $(x, 5)$ is the solution to the system of equations $y = x + 2$ and $y = -x + 8$. What is the value of $x$? ___
5. A point $(c, d)$ is tested and found to be a solution to a system of two linear equations. What does this mean graphically?
- A. The point $(c, d)$ is the y-intercept of both lines.
- B. The point $(c, d)$ is where both lines cross the x-axis.
- C. The point $(c, d)$ is the origin.
- D. The point $(c, d)$ lies on the graph of both lines.
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. The y-intercept of the first line
- C. The slope of the second line
- D. A point that satisfies only one equation
7. The solution to the system of equations $y = 4x$ and $y = x + 6$ is the point $(x, y)$. The solution is ___.
8. Which ordered pair is the solution to the system of equations $y = 3x - 1$ and $y = x + 3$?
- A. (2, 5)
- B. (1, 4)
- C. (0, -1)
- D. (3, 6)
9. Find the solution $(x, y)$ to the system of equations $y = -2x + 5$ and $y = x - 1$. The solution is ___.
10. A student finds that the point $(4, 1)$ satisfies the equation $y = -x + 5$, but not $y = 2x - 9$. What does this mean?
- A. The point lies on the graph of the first line but not the second.
- B. The point is the solution to the system.
- C. The system has no solution.
- D. The student graphed both lines incorrectly.