Solve {l}{a+1500b+8c=122}{a+2000b+5c=130}{a+2200b+10c=158}

$$\left. \begin{array} { l } { a + 1500 b + 8 c = 122 } \\ { a + 2000 b + 5 c = 130 } \\ { a + 2200 b + 10 c = 158 } \end{array} \right.$$

Solve for a, b, c

$$a=30$$

$$b=\frac{1}{25}=0.04$$

$$c=4$$

Short Steps Using Substitution

Solve a+1500b+8c=122 for a.

$$a=122-1500b-8c$$

Substitute 122-1500b-8c for a in the second and third equation.

$$122-1500b-8c+2000b+5c=130 122-1500b-8c+2200b+10c=158$$

Solve these equations for b and c respectively.

$$b=\frac{2}{125}+\frac{3}{500}c c=18-350b$$

Substitute \frac{2}{125}+\frac{3}{500}c for b in the equation c=18-350b.

$$c=18-350\left(\frac{2}{125}+\frac{3}{500}c\right)$$

Solve c=18-350\left(\frac{2}{125}+\frac{3}{500}c\right) for c.

$$c=4$$

Substitute 4 for c in the equation b=\frac{2}{125}+\frac{3}{500}c.

$$b=\frac{2}{125}+\frac{3}{500}\times 4$$

Calculate b from b=\frac{2}{125}+\frac{3}{500}\times 4.

$$b=\frac{1}{25}$$

Substitute \frac{1}{25} for b and 4 for c in the equation a=122-1500b-8c.

$$a=122-1500\times \frac{1}{25}-8\times 4$$

Calculate a from a=122-1500\times \frac{1}{25}-8\times 4.

$$a=30$$

The system is now solved.

$$a=30 b=\frac{1}{25} c=4$$