Question

use a graphing utility to graph the two equations in the system in the same viewing rectangle. then use the intersection feature to display the solution.
$x + y = 6$
$x - y = 4$
use a graphing utility to graph the two equations in the system in the same viewing rectangle. choose the correct graph below
all graphs are $-10,10$ by $-10,10$

Explanation:

Step1: Solve the system of equations

We have the system of equations:

$$\begin{cases} x + y=6\\ x - y=4 \end{cases}$$

Add the two equations together: \((x + y)+(x - y)=6 + 4\).
Simplify the left - hand side: \(x + y+x - y = 2x\), and the right - hand side is \(10\). So, \(2x=10\), then \(x = 5\).
Substitute \(x = 5\) into the first equation \(x + y=6\), we get \(5+y=6\), then \(y=1\). The solution of the system is the point \((5,1)\).

Step2: Analyze the intersection point of the two lines in the graphs

The line \(x + y=6\) can be rewritten as \(y=-x + 6\) (with a slope of \(-1\) and a \(y\) - intercept of \(6\)), and the line \(x - y=4\) can be rewritten as \(y=x - 4\) (with a slope of \(1\) and a \(y\) - intercept of \(-4\)).
The two lines should intersect at the point \((5,1)\).

Answer:

B.