(1) from 1: Y=-a/2X+3.

from 2:Y = 1/ 15X- 1/3。

When k (slope) =115, the equation has no solution.

So:-a/2 =115.

a=-2/ 15

Therefore, when a is not equal to -2/ 15, the equations have a unique solution.

(2) It has been found at (1) that when a is -2/ 15, the equations have no solution.

(3) No solution

Example: Solve the system of equations x+y = 5 16x+ 13y = 89②.

Solution: Take ③ from ① with x=5-y③ to ② to get 6(5-y)+ 13y=89 and y=59/7.

Bring y=59/7 into ③ to get x=5-59/7, that is, x=-24/7.

∴x=-24/7,y=59/7

This solution is the substitution elimination method.

Addition, subtraction and elimination method

Example: Solve the system of equations x+y=5① x-y=9②.

Solution: ①+②, 2x= 14, that is, x=7.

Bring x=7 into ① to get 7+y=5 and y=-2.

∴x=7,y=-2

This solution is addition, subtraction and elimination.

There are three solutions to binary linear equations:

1. There is a solution.

For example, the solution of the equation set X+Y = 5 16x+ 13Y = 89 ② is x=-24/7 and y=59/7.

There are countless solutions.

For example, the equation group X+Y = 6 12x+2Y = 12②, because these two equations are actually an equation (also called "the equation has two equal real roots"), so this equation group has countless solutions.

3. No solution

For example, the equation set X+Y = 4 12x+2Y = 10②, because the simplified equation ② is x+y=5, which contradicts equation ①, so this kind of equation set has no solution.

[Edit this paragraph] ternary linear equation

Definition: Similar to binary linear equation, three combined linear equations contain three unknowns.

Solution of ternary linear equations: similar to binary linear equations, the elimination method is used to eliminate them step by step.