Find the values of a.?
2015-11-17 9:15 am
Two straight lines ax-2y-7=0 and (a-2)x+y-4=0 intersect at a point (a,1).
回答 (1)
2015-11-17 9:24 am
ax - 2y - 7 = 0 ...... ①
(a - 2)x + y- 4 = 0 ...... ②
∵ ①, ② intersect at a point (a,1)
Sub x = a and y = 1 into ①
a (a) - 2(1) - 7 = 0
a² = 9
a = 3 or -3
Sub x = a and y = 1 into ②
(a - 2) (a) + (1) - 4 = 0
a² - 2a - 3 = 0
(a - 3) (a + 1) = 0
a = 3 or -1
∵ ① and ② both pass throuth (a,1) if a = 3
∴ a = 3
(a - 2)x + y- 4 = 0 ...... ②
∵ ①, ② intersect at a point (a,1)
Sub x = a and y = 1 into ①
a (a) - 2(1) - 7 = 0
a² = 9
a = 3 or -3
Sub x = a and y = 1 into ②
(a - 2) (a) + (1) - 4 = 0
a² - 2a - 3 = 0
(a - 3) (a + 1) = 0
a = 3 or -1
∵ ① and ② both pass throuth (a,1) if a = 3
∴ a = 3
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