Solve {l}{a+b+3/2c=6.384}{a+b-3/2c=6.042}{a-26=0.255}

$$\left. \begin{array} { l } { a + b + \frac { 3 } { 2 } c = 6.384 } \\ { a + b - \frac { 3 } { 2 } c = 6.042 } \\ { a - 26 = 0.255 } \end{array} \right.$$

Solve for a, b, c

$$a=26.255$$

$$b=-20.042$$

$$c=0.114$$

Short Steps Using Substitution

Solve a+b+\frac{3}{2}c=6.384 for a.

$$a=-b-\frac{3}{2}c+\frac{798}{125}$$

Substitute -b-\frac{3}{2}c+\frac{798}{125} for a in the second and third equation.

$$-b-\frac{3}{2}c+\frac{798}{125}+b-\frac{3}{2}c=6.042 -b-\frac{3}{2}c+\frac{798}{125}-26=0.255$$

Solve these equations for c and b respectively.

$$c=0.114 b=-\frac{3}{2}c-\frac{19871}{1000}$$

Substitute 0.114 for c in the equation b=-\frac{3}{2}c-\frac{19871}{1000}.

$$b=-\frac{3}{2}\times 0.114-\frac{19871}{1000}$$

Calculate b from b=-\frac{3}{2}\times 0.114-\frac{19871}{1000}.

$$b=-\frac{10021}{500}$$

Substitute 0.114 for c and -\frac{10021}{500} for b in the equation a=-b-\frac{3}{2}c+\frac{798}{125}.

$$a=-\left(-\frac{10021}{500}\right)-\frac{3}{2}\times 0.114+\frac{798}{125}$$

Calculate a from a=-\left(-\frac{10021}{500}\right)-\frac{3}{2}\times 0.114+\frac{798}{125}.

$$a=26.255$$

The system is now solved.

$$a=26.255 b=-\frac{10021}{500} c=0.114$$