Question

When using a graph to solve a system of equations, what is the importance of

the point of intersection?
O a) It determines the slope of the lines
b) It gives the solution to the system
O c) It indicates the y-intercept of the graph
O d) It shows the x-intercept of the graph

Answer 1

The point of intersection on a graph of a system of equations represents the values that satisfy both equations, making it the solution to the system.

Step-by-step explanation:

When using a graph to solve a system of equations, the importance of the point of intersection is that it gives the solution to the system. This is because the point where the two lines intersect is where both equations hold true simultaneously, giving us the values of x and y that satisfy both equations. The slope, represented by m, indicates how steep the line is, and the y-intercept, represented by b in the slope-intercept form equation y = mx + b, is the point where the line crosses the y-axis when x is zero. Thus, for the student's question, the correct answer is that the point of intersection gives the solution to the system of equations (option b).