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Q.

How do you solve the system

2x – 3y = –24 and x + 6y = 18

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a

x = –3, y = 2

b

x = 2, y = 3

c

x = –6, y = 4

d

x = 4, y = 3 

answer is C.

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Detailed Solution

x + 6y = 18
x + 6y – 6y = 18 – 6y
x + 0 = 18 – 6y
x = 18 – 6y …(I)
Putting the value of x in equation (I)
2x – 3y = –2y …(II)
2(18 – 6y) – 3y = –2y
36 – 12y – 3y = –2y
36 + (–12 – 3y) = –2y
36 + (–15y) = –2 y
36 – 15y = –2y
–15y = –24 – 36
+5y = +60y
This putting the value of y to gather value of x
x = 18 – 6y
x = 18 – 6xy
x = 18 – 24
x = –6

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