Chapter 6.1, Problem 2STP

For Exercises $1-4,$ choose the correct letter.

How many solutions does this system have? $2x+y=3$

$6x=9-3y$

F. 1

G. none

H. infinite

I. 2

To determine

To calculate:Solution for $\begin{array}{l}2x+y=3\\ 6x=9-3y\end{array}$ have.

Answer to Problem 2STP

The system has infinite solution.

Explanation of Solution

Given information:

  $\begin{array}{l}2x+y=3\\ 6x=9-3y\end{array}$

Calculation:

  $\begin{array}{l}2x+y=3\mathrm{.......}eq(i)\\ 6x=9-3y\mathrm{......}eq(ii)\end{array}$

From equation (i)

  $2x+y=3$

Therefore,

  $y=3-2x$

Now, putting the value of y in equation (ii) we get-

  $\begin{array}{l}6x=9-3y\\ \Rightarrow 6x=9-3(3-2x)\\ \Rightarrow 6x=9-9+6x\\ \Rightarrow 6x=6x\\ \Rightarrow 0=0\end{array}$

Since,

  $0=0$ for every value of x and y.

So, the system has infinite solution.