If the straight lines x-2y+5=0 and ax-y+1=0 intersect at (1,b),find a and b
Answer is a=2,b=3
If the straight line 2x+y+k=0 passes through the point of intersection of the two straight lines x+y-3=0 and x-y+1=0,find k
Answer is -4
求steps~~~~~~~~
Maths.Equation of line
2010-12-19 11:23 pm
回答 (3)
2010-12-19 11:30 pm
✔ 最佳答案
1 Sub. (1,b) into x-2y+5=0, 1-2b+5=0, b=3. Then sub. (1,3) into ax-y+1=0, a-3+1=0, a=2. So a=2,b=3.
2 x+y-3=0...(1), x-y+1=0...(2)
From (2) y=x+1. Sub. into (1)
x+x+1-3=0
x=1, then y=2
The intersection point of x+y-3=0 and x-y+1=0 is (1,2). Sub. into 2x+y+k=0, we find that k=-4.
2010-12-20 12:34 am
Put (1,b) into x-2y+5=0, we have 1-2b+5=0 2b=6 b=3
Put (1,b) into ax-y+1=0, we have a-b+1=0
Put b=3 into a-b+1=0, we have a-3+1=0 a=2
x+y-3=0 ...i
x-y+1=0 ...ii
i-ii: 2y=4
y=2
Put y=2 into i,
x+2-3=0
x=1
Coordinates of the point of intersection:(1,2)
Put (1,2) into 2x+y+k=0, we have 2+2+k=0 k=-4
Put (1,b) into ax-y+1=0, we have a-b+1=0
Put b=3 into a-b+1=0, we have a-3+1=0 a=2
x+y-3=0 ...i
x-y+1=0 ...ii
i-ii: 2y=4
y=2
Put y=2 into i,
x+2-3=0
x=1
Coordinates of the point of intersection:(1,2)
Put (1,2) into 2x+y+k=0, we have 2+2+k=0 k=-4
2010-12-19 11:44 pm
If the straight lines x-2y+5=0 and ax-y+1=0 intersect at (1,b),find a and b
1-2b-5=0
b=3
_______
a(1)-3+1=0
a=2
____________________________
x+y=3
x-y=-1
y=2,x=1
________
2(1)+2+k=0
k=-4
1-2b-5=0
b=3
_______
a(1)-3+1=0
a=2
____________________________
x+y=3
x-y=-1
y=2,x=1
________
2(1)+2+k=0
k=-4
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