Chapter 6, Problem 9CR

To determine

To find: The solution of the system

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

Answer to Problem 9CR

Infinitely many solutions

Explanation of Solution

Given information: The system of equation

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

Calculation:

The values of x and y is shown in the following table:

Equation	Value of x	Value of y
$y=x+1$	1	2
	2	3
	3	4
$2x-2y=-2$	1	2
	2	3
	3	4

From the table it is observed, both the straight lines pass through the same points.

The graphs of the straight lines $y=x+1$ and $2x-2y=-2$ are drawn on the same co-ordinate plane and it is observed the lines coincide.

The two systems of equations represent the same straight line. So, every points lying on the line is a solution of the system.

Hence, the system of equation has infinitely many solutions.