Question

Graphical Method

Two equations and their graphs are given. Find the intersection point(s) of the graphs by solving the system.

$\left\{\begin{array}{l}x+y=2\\ 2x+y=5\end{array}\right.$

Short answer

Hence, the intersection points of the graphs by solving the system are $x=3\&y=-1$

Step-by-step solution

Step 1. Given information

We are given the system of linear equations that is-

$\left\{\begin{array}{l}x+y=2\\ 2x+y=5\end{array}\right.$

Step 2. Concept used

The system of linear equations is the collection of one or more linear equations involving the same set of variables.

We need to find the intersection points of the graphs by solving the system. By the Graphical Method, we will calculate the result.

Step 3. Calculation

We Subtract the second equation from the first equation to eliminate the y term.

$\begin{array}{l}(x-2x)+(y-y)=2-5\\ -x=-3\\ x=3\end{array}$

We substitute the value of x in any of the original equations to get back the value of y.

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