Chapter SH, Problem 6.7EP

To determine

To solve system of equation using substitution

  $-2y=x+3$

  $\frac{3}{2}=-\frac{1}{2}x-y$

Answer to Problem 6.7EP

The system of equation having many solutions.

Explanation of Solution

Given information:

  $-2y=x+3$

  $\frac{3}{2}=-\frac{1}{2}x-y$

Calculation:

  $-2y=x+3\mathrm{..........}(1)$

  $\frac{3}{2}=-\frac{1}{2}x-y$ .............(2)

From equation (1) on substitution $y=\frac{x+3}{-2}$ in equation (2)

  $\frac{3}{2}=-\frac{1}{2}x-(\frac{x+3}{-2})$

On solving,

  $\frac{3}{2}=-\frac{1}{2}x+\frac{x}{2}+\frac{3}{2}$

On soiving,

  $x=x$

There are infinite number of values of x make above equation true.

Hence, the system of equation having many solutions.