https://file.aiquickdraw.com/mathbot/file/1725399342092rbbtx01x.jpg

wo lines, P and Q, are graphed:

Determine the solution and the reasoning that justifies the solution to the systems of equations. (1 point)

(0, 8), because this point is true for both equations

(0, 8), because the lines intersect the y-axis at these points

(−2, 4), because this point makes both equations incorrect

(−2, 4), because it is the point of intersection of the two graphs

The correct solution to the system of equations represented by the two lines in the graph is the point \((-2, 4)\). This is because \((-2, 4)\) is the point where the two lines intersect. 

In a system of linear equations, the solution is the point where the two lines meet, as it satisfies both equations simultaneously. The other options are incorrect because:

- \((0, 8)\) is not the intersection point; it is where one of the lines intersects the y-axis.
- The statement that \((-2, 4)\) makes both equations incorrect is false; in fact, it makes both equations true, which is why it is the solution.

Therefore, the correct answer is:
- **\((-2, 4)\), because it is the point of intersection of the two graphs.**

Would you like more details or have any other questions? Here are some additional related questions:

1. What is the method for finding the intersection point of two lines algebraically?
2. How can you determine the equation of a line given its graph?
3. What does the slope of a line represent, and how is it calculated?
4. How do you solve a system of linear equations using substitution?
5. What is the graphical interpretation of a system of linear equations with no solution?

**Tip:** When solving systems of equations graphically, always look for the intersection point, as it represents the solution where both equations hold true.

Two lines, P and Q, are graphed: Determine the solution and the reasoning that justifies the solution to the systems of equations. (1 point)

(0, 8), because this point is true for both equations
(0, 8), because the lines intersect the y-axis at these points
(−2, 4), because this point makes both equations incorrect
(−2, 4), because it is the point of intersection of the two graphs

Learn how to determine the solution to a system of linear equations graphically by finding the point of intersection. This example uses lines P and Q to explore key algebraic concepts and is ideal for students in Grades 8-10.

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