Solve for: {\text{begin}array l x+y=1 } 2x-y=5\text{end}array .

Expression: $\left\{\begin{array} { l } x+y=1 \\ 2x-y=5\end{array} \right.$

Move the variable to the right-hand side and change its sign

$\left\{\begin{array} { l } y=1-x \\ 2x-y=5\end{array} \right.$

Move the variable to the right-hand side and change its sign

$\left\{\begin{array} { l } y=1-x \\ -y=5-2x\end{array} \right.$

Multiply both sides of the equation by $-1$

$\left\{\begin{array} { l } y=1-x \\ y=-5+2x\end{array} \right.$

Since both expressions $1-x$ and $-5+2x$ are equal to $y$, set them equal to each other forming an equation in $x$

$1-x=-5+2x$

Solve the equation for $x$

$x=2$

Substitute the given value of $x$ into the equation $y=-5+2x$

$y=-5+2 \times 2$

Solve the equation for $y$

$y=-1$

The possible solution of the system is the ordered pair $\left( x, y\right)$

$\left( x, y\right)=\left( 2, -1\right)$

Check if the given ordered pair is the solution of the system of equations

$\left\{\begin{array} { l } 2+\left( -1 \right)=1 \\ 2 \times 2-\left( -1 \right)=5\end{array} \right.$

Simplify the equalities

$\left\{\begin{array} { l } 1=1 \\ 5=5\end{array} \right.$

Since all of the equalities are true, the ordered pair is the solution of the system

$\left( x, y\right)=\left( 2, -1\right)$