Determine whether the system of linear equations has one and only one solution, infinitely many solutions, or no solution. Find all solutions whenever they exist.

x + 3y = 9

3x - y = 7

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using elimination method

x + 3y =9--------------i

3x -y = 7-------------ii

eliminating x

we multiply equation i with 3 and ii with 1 to give us

3x + 9y = 27 -------------------- iii

3x - y = 7 ----------------------iv

subtracting iv from iii

10y = 20

y=2

thus x can be found by substituting the value of y in i

x + 3 (2) = 9

x +6 =9

x= 9-6

x = 3

thus they have only one solution (3, 2)

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