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Question
Solve each of the following systems of equations by the method of cross-multiplication :
2x + y = 35
3x + 4y = 65
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Solution
The given system of equations may be written as
2x + y - 35 = 0
3x + 4y - 65 = 0
Here
`a_1 = 2, b_1 = 1, c_1 = -35`
`a_2 = 3, b_2 = 4, and c_2 = -65`
By cross multiplication, we have
`=> x/(1xx (-65) - (-35) xx 4) = (-y)/(2xx(-65)-(-35)xx3) = 1/(2xx4 - 1xx3)`
`=> x/(-65 + 140) = (-y)/(-130 + 105) = 1/(8 -3)`
`=> x/75 = (-y)/(-25) = 1/5`
`=> x/75 = y/25 = 1/5`
Now
`y/25 = 1/5`
`=> y = 25/5 =5`
Hence, x = 15, y = 5is the solution of the given system of equations.
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