Question

Why we can't use simultaneous linear equation method

Answer 1

Solve simultaneously for x and y:

x + y = 10

x − y = 2

This means that we must find values of x and y that will solve both equations.  We must find two numbers whose sum is 10 and whose difference is 2.

The two numbers, obviously, are 6 and 4:

6 + 4 = 10

6 − 4 = 2

Let us represent the solution as the ordered pair (6, 4).

Now, these two equations --

x + y = 10

x − y = 2

-- are linear equations (Lesson 33).  Hence, the graph of each one is a straight line.  Here are the two graphs:

simultaneous equations

The solution to the simultaneous equations is their point of intersection.  Why?  Because that coördinate pair solves both equations. (Lesson 33.)  That point is the one and only point on both lines.