Chapter 10.8, Problem 34E

To determine

To find: The solutions to the system of equations

Answer to Problem 34E

The solution to the system of equations is

Explanation of Solution

Given:

  $y=x^2-4x$

  $2x-y=2$

Calculation:

Consider the system of equations

  $y=x^2-4x$ Equation $1$

  $2x-y=2$ Equation $2$

Need to find all the solutions of the system by the graphical method

Solve the second equation for $y$

  $2x-y=2$

  $2x=2+y$ Adding $y$ to both sides

  $y=2x-2$ Subtracting $2$ from both sides

Here the graph is drawn using $TI-83$ calculator

Press on $Y=$ button and enter the functions:

  

Press on WINDOW button and set the viewing rectangle:

  

Press on GRAPH button to get the graph of the functions:

  

From this graph, observe that the system has two points of intersection in quadrants I and IV .

For finding those points, follow the procedure:

Round to the two decimal places set the graphing calculator as follows,

Press MODE then set FLOAT up to 2 then press ENTER

  

Press $2nd$ button and then press on TRACE button. The following options are displayed on the screen

  

In these options select the option number $5:\mathrm{int}\text{ersect}$

After that use the left and right buttons to confirm the first and second curves by pressing

  

Therefore, one of the intersecting points is $(0.35,-1.29)$

To find the other point of intersection

  

Therefore, the intersecting point is $(5.65,9.29)$

Hence the solutions to the system of equations are $\text{(0}\text{.35,-1}\text{.29) and (5}\text{.65,9}\text{.29)}$

Conclusion:

The solution to the system of equations is

  $\text{(0}\text{.35,-1}\text{.29) and (5}\text{.65,9}\text{.29)}$