Solve {l}{x_{1}-x_{2}+x_{3}+x_{4}=7}{x_{2}-x_{3}+x_{4}=0}{x_{3}-x_{4}=1}{x_{4}=11}

$$\left. \begin{array}{l}{ x _ { 1 } - x _ { 2 } + x _ { 3 } + x _ { 4 } = 7 }\\{ x _ { 2 } - x _ { 3 } + x _ { 4 } = 0 }\\{ x _ { 3 } - x _ { 4 } = 1 }\\{ x _ { 4 } = 11 }\end{array} \right.$$

Solve for x_1, x_2, x_3, x_4

$$x_{1}=-15$$

$$x_{2}=1$$

$$x_{3}=12$$

$$x_{4}=11$$

Solution Steps

Consider the third equation. Insert the known values of variables into the equation.

$$x_{3}-11=1$$

Add 11 to both sides.

$$x_{3}=1+11$$

Add 1 and 11 to get 12.

$$x_{3}=12$$

Consider the second equation. Insert the known values of variables into the equation.

$$x_{2}-12+11=0$$

Add -12 and 11 to get -1.

$$x_{2}-1=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$x_{2}=1$$

Consider the first equation. Insert the known values of variables into the equation.

$$x_{1}-1+12+11=7$$

Add -1 and 12 to get 11.

$$x_{1}+11+11=7$$

Add 11 and 11 to get 22.

$$x_{1}+22=7$$

Subtract 22 from both sides.

$$x_{1}=7-22$$

Subtract 22 from 7 to get -15.

$$x_{1}=-15$$

The system is now solved.

$$x_{1}=-15 x_{2}=1 x_{3}=12 x_{4}=11$$