Verify that the following pair of equations has a unique solution and find the
solution: ax + by + p = 0, ax − cy − q = 0
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Answer:
ax+by = -p
ax = - by - p
x = -(b+p) /a
now putting the value of x in the following
ax - cy = q
a*-(b+p) /a - cy = q
-(b+p) - cy = q
multiplying by -1 both sides
b+p+cy = -q
cy = - q - b - p
cy = -(b+p+q)
y = - (b+p+q) /c
hence,
x = -(b+p) /a ; y = - (b+p+q) /c
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