Chapter 2, Problem 1FCCE

What is meant by a solution to a system of linear equations?

To determine

The meaning of the solution to a system of linear equations.

Answer to Problem 1FCCE

Solution:

A solution to the system of linear equations is the point of intersection of line or plane corresponding to equations in the system or is the value of the variables takes as x, y, z.

Explanation of Solution

A system of linear equations represents line or plane and the point where they intersect is the solution of the system as that point satisfies all the equations in the system.

That is, the intersection is the value of the variables.

For example:

Consider a system of linear equations,

$\begin{array}{l}x+y=1\\ x-y=1\end{array}$

On solving the above equation as:

$\begin{array}{r}\underset{\_}{\begin{array}{l}x+y=1\\ x-y=1\end{array}}\\ 2x=2\\ x=1\end{array}$

And,

Put $x=1$ in any one of the equations,

So,

$\begin{array}{c}x+y=1\\ 1+y=1\\ y=0\end{array}$

This system represents two lines and they intersect at point $\left(1,0\right)$.

Therefore, the solution of the system of linear equation is the value of the variables.