SOLUTION: algebracially solve the system of equations. show your work. ax-by=b+a bx+ay=b+a

Algebra ->  Matrices-and-determiminant -> SOLUTION: algebracially solve the system of equations. show your work. ax-by=b+a bx+ay=b+a      Log On


   

Question 422028: algebracially solve the system of equations. show your work.
ax-by=b+a
bx+ay=b+a
Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
The key here is to eliminate one variable so we can solve for the other. So I'm going to eliminate y.


ax-by=b+a
bx+ay=b+a



a^2x-aby=ab+a^2
b^2x+aby=b^2+ab

Note: I multiplied both sides of the first equation by 'a' and both sides of the second equation by 'b'


Now add the two equations to get


a^2x+b^2x=a^2+2ab+b^2


(a^2+b^2)x=a^2+2ab+b^2


x=(a^2+2ab+b^2)/(a^2+b^2)


Now that we know that x=(a^2+2ab+b^2)/(a^2+b^2), we can use it to solve for 'y'. I'll let you do that.