Chapter 9.1, Problem 12WE

To determine

To find: The solution of the given two linear equations by the graphing method.

Answer to Problem 12WE

The system has infinite many solutions.

Explanation of Solution

Given:

The given equations are:

  $\begin{array}{c}6x+4y=2\dots \left(1\right)\\ 3x+2y=1\dots \left(2\right)\end{array}$

As the slope of the equations $\left(1\right)$ and $\left(2\right)$ is $\frac{-3}{2}$ and the $y$ -intercept of the equations $\left(1\right)$ & $\left(2\right)$ is $\frac{1}{2}$ .

So, the graphs of the given equations are coincide

To solve the given equations by graphing method, first, make the tables of the corresponding values of $y$ after substituting the randomly selected values of $x$ in the given equations.

The table for the equation $6x+4y=2$ is given as:

Table1

$x$	$0$	$1$
$y$	$0.5$	$-1$

The table for the equation $3x+2y=1$ is given as:

Table2

$x$	$0$	$1$
$y$	$0.5$	$-1$

Plot all the ordered pairs that shows in the table1 and table2 and hence join them to make the lines in the coordinate plane.

So the graph is given as:

  

As the graphs of two given equations are coincide, so the given system has infinite many solutions.

Therefore, the system has infinite many solutions.