Question

solutions for intersecting lines in graph​

Answer 1

Answer:

Graphing equations in order to identify a specific point of intersection is usually not a precise way to solve systems because it is often difficult to see exactly where two lines intersect (unless you are using a computer-based graphing program that allows you to zoom in on a point). However, the graph of a system of equations can still give a good idea of what type of solution, if any, exists. Let’s graph a system, and see how it works.

Graph the system y = 3x and x + 2y = 4. How many solutions does this system have?

A graph of the two lines y = 3x and x + 2y = 4 shows us that the lines intersect, meaning that there is a single (x, y) value that satisfies both equations. Looking at the graph does not tell us exactly where that point is, but we don’t need to know that information here, because the question only asks for the number of solutions.

So a system made of two intersecting lines has one solution. Now let’s look at a different situation:

Answer 2

Answer:

In this case the two equations describe lines that intersect at one particular point. Clearly this point is on both lines, and therefore its coordinates (x, y) will satisfy the equation of either line. Thus the pair (x, y) is the one and only solution to the system of equations.