This is a system of two equations and two variables. We consider a and b in these equations two different numbers that are given and do not change. We call these coefficients.
We will solve the system using elimination method.
ax + by=a
ax - by =b
We add the two equations. Coefficients in front of y variable are opposite numbers and add up to zero. The resulting equation has only one variable: x.
2ax = a+b
x = (a+b)/(2a)
Next, we can subtract the two equations and the resulting equation has only the variable y.
2by = a-b
y = (a-b)/(2b)
Note, the parameters a and b are in the denominator of the expressions of the solutions of the variables x and y. The solution exists only if
a
and
b
are not equal to zero.
