Chapter 7.1, Problem 54E

To determine

Solve the system graphically or algebraically. Explain your choice of method.

  $\{\begin{array}{c}x-2y=1\\ y=\sqrt{x-1}\end{array}$

Answer to Problem 54E

The solution for the equations given is $x=5,y=2$ and $x=1,y=0$

Explanation of Solution

Given:

The given equations are $\{\begin{array}{c}x-2y=1\\ y=\sqrt{x-1}\end{array}$

Concept Used:

The given equations are in two variables x and y. These equations can be solved using graphical method and algebraic method. This equations are complex so they can be solved graphically.

By substituting some random x values in the equation we get y values and they are plotted on the graph and the exact point is found.

Calculation:

When we draw these two equations on a graph they meet at a point and it is the solution of these equations. If they do not meet then it is considered as inconsistent and will have no solution.

The graph plotted by these equations is as follows

  

Both the equations are satisfied at the point they meet which is $x=5,y=2$ and $x=1,y=0$

We can know this by substituting this values in the equation above.

  $\begin{array}{l}x-2y=1\\ 5-2(2)=1\\ 1=1\end{array}$

And

  $\begin{array}{l}x-2y=1\\ 1-2(0)=1\\ 1=1\end{array}$

Conclusion:

The solution for the equations given is $x=5,y=2$ and $x=1,y=0$