Chapter 8.10, Problem 2CYU

To determine

The solution of the $y=x+1$ and $x+y=7$ by using the graphing method

Answer to Problem 2CYU

The solution of $y=x+1$ and $x+y=7$ is $x=3,y=4$

Explanation of Solution

Given:

The two eqn are as:

  $\begin{array}{l}y=x+1\\ x+y=7\end{array}$

Calculation:

The two eqns. are described as:

  $y=x+1$..........(1)

  $x+y=7$..........(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. $y=x+1$

  

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

  $\begin{array}{l}x+y=7\\ y=-x+7\end{array}$

Now, draw a graph of $y=-x+7$ :

  

From graph of two equations; understands that these two lines intersects at the point $\left(3,4\right)$

So, the point of intersection $\left(3,4\right)$ is the solution of equation sets $\begin{array}{l}y=x+1\\ x+y=7\end{array}$

The solution is $x=3,y=4$

Conclusion:

Hence, there is one solution for the given equation set which is its point of intersection.