Solve {l}{b+c=4}{a+c=5}{a+b=6}

$$\left\{ \begin{array} { l } { b + c = 4 } \\ { a + c = 5 } \\ { a + b = 6 } \end{array} \right.$$

Solve for b, c, a

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

$$c = \frac{3}{2} = 1\frac{1}{2} = 1.5$$

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

Short Steps Using Substitution

Solve b+c=4 for b.

$$b=-c+4$$

Substitute -c+4 for b in the equation a+b=6.

$$a-c+4=6$$

Solve the second equation for c and the third equation for a.

$$c=-a+5 a=c+2$$

Substitute -a+5 for c in the equation a=c+2.

$$a=-a+5+2$$

Solve a=-a+5+2 for a.

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

Substitute \frac{7}{2} for a in the equation c=-a+5.

$$c=-\frac{7}{2}+5$$

Calculate c from c=-\frac{7}{2}+5.

$$c=\frac{3}{2}$$

Substitute \frac{3}{2} for c in the equation b=-c+4.

$$b=-\frac{3}{2}+4$$

Calculate b from b=-\frac{3}{2}+4.

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

The system is now solved.

$$b=\frac{5}{2} c=\frac{3}{2} a=\frac{7}{2}$$