Question

(04.01 mc)
two lines, a and b, are graphed:
image of two lines a (blue) and b (red) graphed on a coordinate plane
determine the solution and the reasoning that justifies the solution to the systems of equations. (1 point)
○ (-4, 6), because both the equations are true for this point
○ (2, 8), because the graph of the two equations intersects at this point
○ (2, 8), because neither of the two equations is true for this coordinate point
○ (-4, 6), because the graph of the two equations intersects the axis at these points

Explanation:

Step1: Recall System Solution

The solution to a system of linear equations graphed as two lines is the point where they intersect, as that point satisfies both equations.

Step2: Identify Intersection

From the graph, lines A and B intersect at (2, 8). Now check the options:

• First option: (-4,6) is not the intersection, eliminate.
• Second option: (2,8) is the intersection, so it's the solution (satisfies both equations), and the reasoning about intersection is correct.
• Third option: Reasoning is wrong (intersection point satisfies both equations).
• Fourth option: (-4,6) is not intersection, and reasoning about axis intersection is wrong.

Answer:

B. (2, 8), because the graph of the two equations intersects at this point