Chapter 8.10, Problem 3CYU

To determine

The solution of the $y=\frac{3}{2}x-1$ and $3x-2y=2$ by using the graphing method

Answer to Problem 3CYU

There is no solution for the system of two equations $y=\frac{3}{2}x-1$ and $3x-2y=2$

Explanation of Solution

Given:

The two eqn are as:

  $\begin{array}{l}y=\frac{3}{2}x-1\\ 3x-2y=2\end{array}$

Calculation:

The two eqns. are described as:

  $y=\frac{3}{2}x-1$..........(1)

  $3x-2y=2$..........(2)

Now, need to draw the graph of the first equation which is already in $y$ - intercept form. So, check the following graph for the first eq. $y=\frac{3}{2}x-1$

  

Now, need to rewrite the second equation into the $y$ - intercept form:

  $\begin{array}{l}y=x+4\\ y=0+4\\ y=4\end{array}$

Now, draw a graph of $y=\frac{3}{2}x+1$ :

  

From graph of two equations; understands that these two lines are non-coincident or parallel to each other that mean there is no solution for $y=\frac{3}{2}x-1,y=\frac{3}{2}x+1$ .

Conclusion:

Hence, there is no solution for the given system of equations.