intersecting lines are consistent(independent)??

consistent(independent)---> intersecting lines

If the equations on a give equation have they only have one solution
a1/a2 is not equal to b1/b2 is not equal to c1/c2<<< construction of the coefficient of the variables in the equations

Problem
Find all solutions to the system y – x = 1 and y + x = 3.

First, graph both equations on the same axes.
 The two lines intersect once. That means there is only one solution to the system.

The point of intersection appears to be (1, 2).
Read the point from the graph as accurately as possible.

y – x = 1
2 – 1 = 1
1 = 1

TRUE

(1, 2) is a solution of y – x = 1.
y + x = 3
2 + 1 = 3
3 = 3

TRUE

(1, 2) is a solution of y + x = 3.
Check the values in both equations. Substitute 1 for x and 2 for y. (1, 2) is a solution.
Answer
(1, 2) is the solution to the system y – x = 1 and
y + x = 3.
Since (1, 2) is a solution for each of the equations in the system, it is the solution for the system.