Solve the system by graphing:$\left\{\begin{array}{l}2x+y=6\\ x+y=1\end{array}\right.$$\left\{\begin{array}{l}2x+y=6\\ x+y=1\end{array}\right.$

We are given a system of equations $\left\{\begin{array}{l}2x+y=6\\ x+y=1\end{array}\right.$and we need to find its solution by graphing.

Solving the equation $2x+y=6$for $y$we get,

$\begin{array}{rcl}2x+y-2x& =& 6-2x\\ y& =& -2x+6\end{array}$

So the slope of the line is $-2$and its $y$intercept is $6$. Using this the graph of the equation is given as

Solving the equation $x+y=1$for $y$we get,

$\begin{array}{rcl}x+y-x& =& 1-x\\ y& =& -x+1\end{array}$

So the slope of the line is $-1$and its $y$intercept is 1.

So its graph can be drawn on the same plane as,

From the graph, it can be seen that the two lines intersect at the point $(5,-4)$.

So the point$(5,-4)$is the solution to the given system.

Substitute 5 for $x$and $-4$for $y$in the first equation.

It is a true statement.

Again, substitute the values in the second equation.

This is also a true statement.

So the point satisfies both the equations.