Solution: Derive from known conditions.
( 1)-2a+b= 1
(2)-2b+a=7
( 1)+(2):-a-b=8
a+b=-8
( 1)-(2):-3a+3b=-6
a-b=2
Then (a+b)(a-b)=- 16.
2. If the solution of x+y = a and x-y = 4a is the solution of the binary linear equation 3x-5y-30=0, then a is equal to.
Solution: obtained from the first two equations: x=5/2*a, y=-3/2*a substituted into the following formula:
15/2*a+ 15/2*a-30=0
Solution: a=2
3. If the two solutions of ax+by+2=0 are x= 1, y=- 1 and X = 2, Y = 2, then the equation has other solutions.
Solution: Substitute two solutions into the equation:
a-b+2=0
2a+2b+2=0
The solution is a=-3/2.
b= 1/2
So: -3/2*x+ 1/2*y+2=0.
Then the equation has infinite solutions, such as X=0, Y=-4 and so on.