Solve {l}{-x_{a}+y=lambda}{x_{1}-xy=-11}

$$\left\{ \begin{array} { l } { - x _ { a } + y = \lambda } \\ { x _ { 1 } - x y = - 11 } \end{array} \right.$$

Solve for x, y (complex solution)

$$\left\{\begin{matrix}x=\frac{x_{1}+11}{x_{a}+\lambda }\text{, }y=x_{a}+\lambda \text{, }&x_{a}\neq -\lambda \\x\in \mathrm{C}\text{, }y=0\text{, }&x_{1}=-11\text{ and }x_{a}=-\lambda \end{matrix}\right.$$

Steps Using Substitution

Pick one of the two equations which is more simple to solve for y by isolating y on the left hand side of the equal sign.

$$y-x_{a}=\lambda$$

Add x_{a} to both sides of the equation.

$$y=x_{a}+\lambda$$

Substitute \lambda +x_{a} for y in -yx+x_{1}=-11. Because the resulting equation contains only one variable, you can solve for x directly.

$$-\left(x_{a}+\lambda \right)x+x_{1}=-11$$

Multiply -1 times \lambda +x_{a}.

$$\left(-\left(x_{a}+\lambda \right)\right)x+x_{1}=-11$$

Divide -11-x_{1} by -\left(\lambda +x_{a}\right).

$$x=\frac{x_{1}+11}{x_{a}+\lambda }$$

The system is now solved.

$$y=x_{a}+\lambda ,x=\frac{x_{1}+11}{x_{a}+\lambda }$$

Solve for x, y

$$\left\{\begin{matrix}x=\frac{x_{1}+11}{x_{a}+\lambda }\text{, }y=x_{a}+\lambda \text{, }&x_{a}\neq -\lambda \\x\in \mathrm{R}\text{, }y=0\text{, }&x_{1}=-11\text{ and }x_{a}=-\lambda \end{matrix}\right.$$

Steps Using Substitution

Pick one of the two equations which is more simple to solve for y by isolating y on the left hand side of the equal sign.

$$y-x_{a}=\lambda$$

Add x_{a} to both sides of the equation.

$$y=x_{a}+\lambda$$

Substitute \lambda +x_{a} for y in -yx+x_{1}=-11. Because the resulting equation contains only one variable, you can solve for x directly.

$$-\left(x_{a}+\lambda \right)x+x_{1}=-11$$

Multiply -1 times \lambda +x_{a}.

$$\left(-\left(x_{a}+\lambda \right)\right)x+x_{1}=-11$$

Divide -11-x_{1} by -\left(\lambda +x_{a}\right).

$$x=\frac{x_{1}+11}{x_{a}+\lambda }$$

The system is now solved.

$$y=x_{a}+\lambda ,x=\frac{x_{1}+11}{x_{a}+\lambda }$$