Solve {l}{a-b+c=1}{a+b+c=7}{2a+b=9}

$$\left\{ \begin{array} { l } { a - b + c = 1 } \\ { a + b + c = 7 } \\ { 2 a + b = 9 } \end{array} \right.$$

Solve for a, b, c

$$a=3$$

$$b=3$$

$$c=1$$

Short Steps Using Substitution

Solve a-b+c=1 for a.

$$a=b-c+1$$

Substitute b-c+1 for a in the second and third equation.

$$b-c+1+b+c=7 2\left(b-c+1\right)+b=9$$

Solve these equations for b and c respectively.

$$b=3 c=-\frac{7}{2}+\frac{3}{2}b$$

Substitute 3 for b in the equation c=-\frac{7}{2}+\frac{3}{2}b.

$$c=-\frac{7}{2}+\frac{3}{2}\times 3$$

Calculate c from c=-\frac{7}{2}+\frac{3}{2}\times 3.

$$c=1$$

Substitute 3 for b and 1 for c in the equation a=b-c+1.

$$a=3-1+1$$

Calculate a from a=3-1+1.

$$a=3$$

The system is now solved.

$$a=3 b=3 c=1$$