1.

If `3x - 2y = 12 and 6x + y = 9`, then find the values of x and y

Answer» `3x - 2y = 12` (1)
`6x + y = 9` (2)
Using this method, the two equations are reduced to a single variable equation by substituting the value of one variable, obtained from one equation, in the other equation
Step1: Using the first equation, find x in terms of y, i.e., `3x - 2y = 12 rArr 3x = 12 + 2y`
`rArr x = (12 + 2y)/(3)` (3)
Step2: Substitute the value of x in the second equatio to find the value of y, i.e., `6x + y = 9`
`rArr 6((12 + 2y)/(3)) + y = 9`
Step 3: Simplify the equation in terms of y and find the value of y
`2(12 + 2y) + y = 9`
`rArr 24 + 4y + y = 9`
`rArr 5y = 9 - 24`
`rArr y = -3`
Step4 : Substituting the value of y in Eq. (3) we get `x = 2`
`:.` The solution for the given pair of equations is (x, y) i.e., `(2, -3)`


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