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Question
Solve each of the following systems of equations by the method of cross-multiplication
2x − y = 6
x − y = 2
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Solution
The given system of equations may be written as
2x − y - 6 = 0
x − y - 2 = 0
Here
`a_1 = 2, b_1 = -1, c_1 = -6`
`a_2 = 1, b_2 = -1, c _2 = -2`
By cross multiplication, we get
`=> x/((-1)xx(-2)-(-6)xx(-1)) = (-y)/(2xx(-2)-(-6)xx1)= 1/(2xx (-1) -( -1)xx1)`
`=> x/(2-6) = (-y)/(-4+6)= 1/(-2 + 1)`
`=> x/(-4) = (-y)/2 = 1/(-1)`
`=> x/(-4) = (-y)/2 = 1`
Now
`x/(-4) = -1`
`=> x = (-4) xx (-1) = 4`
And
`(-y)/2 = -1`
`=> (-y) = (-1) xx 2`
=> -y = -2
=> y = 2
Hence, x = 4, y = 2 is the solution of the given system of the equations
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