There are three unknowns, each of which has a degree. Such an integral equation is called a ternary linear equation.

* * * A set of integral equations composed of three ternary linear equations is called ternary linear equations.

Solution example

2x-y+z= 10 ①

3x+2y-z= 16 ②

x+6y-z=28 ③

Analysis: Solving a ternary linear equation is similar to solving a binary linear equation, and it is better to choose an unknown with simpler coefficients when eliminating elements. Considering the coefficient characteristics of unknowns in the above-mentioned ternary linear equations, it is relatively simple to eliminate z first.

Solution: ①+②, 5x+y=26④.

①+③，3x+5y=38⑤

④ and ⑤ form an equation:

Solve this system of equations and get x and y values.

Substituting into formula ③, it is convenient to calculate and get the z value.

Note: In order to transform the ternary linear equations into binary linear equations, each equation in the original equations must be used at least once.

Can choose simple and special solutions to solve special ternary linear equations.