Solve the following pairs of equations by reducing them to a pair of linear equations:
The given pair of linear equations are:
6x + 3y = 6xy
2x + 4y = 5xy
These are not linear equations in the variables x and y but can be reduced to linear equations by an appropriate substitution.
If we put x = 0 in either of the two equations, we get y = 0.
So, x = 0 and y = 0 form a solution of the given system of equations.
To find the other solutions, assume that .
On dividing each of the given equations by xy, we have:
The above equations become:
6u + 3v = 6 ... (1)
2u + 4v = 5 ... (2)
Multiplying equation (2) by 3, we get,
6u + 12v = 15 ... (3)
Subtracting equation (1) from equation (3), we have:
9v = 9 v = 1
From equation (1):
6u + 3v = 6 6u + 3.1 = 6 6u = 3 u = Hence, x = 1, y = 2
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