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Question
Solve each of the following systems of equations by the method of cross-multiplication :
x + 2y + 1 = 0
2x − 3y − 12 = 0
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Solution
The given system of equation is
x + 2y + 1 = 0
2x − 3y − 12 = 0
Here
`a_1 = 1, b_1 = 2, c_1 = 1`
`a_2 = 2, b_2 = -3, c_3 = -12`
By cross-multiplication, we get
`=> x/(2xx(-12)-1xx(-3)) = (-y)/(1 xx (-12) - 1 xx 2) = 1/(1xx (-3) - 2xx2)`
`=> x/(-24 + 3) = (-y)/(-12 - 2) = 1/(-3-4)`
`=> x/(-21) = (-y)/(-14) = 1/(-7)`
Now
`x/(-21) = 1/(-7)`
`=> x = (-21)/7 = 3`
and
`(-y)/(-14) = 1/-7`
`=> y/14 = (-1)/7`
`=> y = (-14)/7 = -2`
Hence, the solution of the given system of equations is x = 3 and y = -2
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