Solve the following pair of linear equations by the substitution method
3x – y = 3
9x – 3y = 9
3x - y = 3 (1)
9x - 3y = 9 (2)
From (1), we obtain
y = 3x - 3 (3)
Substituting this value in equation (2), we obtain
9x - 3(3x - 3) = 9
9x - 9x + 9 = 9
9 = 9
This is always true.
Hence, the given pair of equations has infinite possible solutions and the relation between these variables can be given by y = 3x - 3
Therefore, one of its possible solutions is x = 1, y = 0.
Concept: Algebraic Methods of Solving a Pair of Linear Equations - Substitution Method
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