Solve {l}{x_{1}-x_{2}=a}{(3/4x_{1}-1)=a}{-x_{2}+6=a}

$$\left. \begin{array} { l } { x _ { 1 } - x _ { 2 } = a } \\ { ( \frac { 3 } { 4 } x _ { 1 } - 1 ) = a } \\ { - x _ { 2 } + 6 = a } \end{array} \right.$$

Solve for x_1, x_2, a

$$x_{1}=6$$

$$x_{2} = \frac{5}{2} = 2\frac{1}{2} = 2.5$$

$$a = \frac{7}{2} = 3\frac{1}{2} = 3.5$$

Short Steps Using Substitution

Solve x_{1}-x_{2}=a for a.

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

Substitute x_{1}-x_{2} for a in the second and third equation.

$$\frac{3}{4}x_{1}-1=x_{1}-x_{2} -x_{2}+6=x_{1}-x_{2}$$

Solve these equations for x_{2} and x_{1} respectively.

$$x_{2}=1+\frac{1}{4}x_{1} x_{1}=6$$

Substitute 6 for x_{1} in the equation x_{2}=1+\frac{1}{4}x_{1}.

$$x_{2}=1+\frac{1}{4}\times 6$$

Calculate x_{2} from x_{2}=1+\frac{1}{4}\times 6.

$$x_{2}=\frac{5}{2}$$

Substitute \frac{5}{2} for x_{2} and 6 for x_{1} in the equation a=x_{1}-x_{2}.

$$a=6-\frac{5}{2}$$

Calculate a from a=6-\frac{5}{2}.

$$a=\frac{7}{2}$$

The system is now solved.

$$x_{1}=6 x_{2}=\frac{5}{2} a=\frac{7}{2}$$