Solve the system by graphing:$\left\{\begin{array}{l}-x+y=1\\ 2x+y=10\end{array}\right.$$\left\{\begin{array}{l}-x+y=1\\ 2x+y=10\end{array}\right.$

We are given a system of equations$\left\{\begin{array}{l}-x+y=1\\ 2x+y=10\end{array}\right.$ and we need to find its solution by graphing.

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 $y$intercept is 1. Using this the graph of the equation is given as,

Solving the equation $2x+y=10$for $y$we get,

$\begin{array}{rcl}2x+y-2x& =& 10-2x\\ y& =& -2x+10\end{array}$

So the slope of the line is $-2$and its $y$intercept is 10.

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 $(3,4)$.

So, the point$(3,4)$is the solution to the given system.

Substitute 3 for $x$and 4 for $y$in the first equation.

$\begin{array}{rcl}-x+y& =& 1\\ -3+4& =& 1\\ 1& =& 1\end{array}$

It is a true statement.

Again, substitute the values in the second equation.

$\begin{array}{rcl}2x+y& =& 10\\ 2·3+4& =& 10\\ 6+4& =& 10\\ 10& =& 10\end{array}$

This is also a true statement.

So the point satisfies both the equations.