If 2x − 3y=7 and (a+b)x − (a+b − 3)y = 4a+b
represent coincident lines then a and b satisfy the
equation
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Answers
Answer:
The required equation satisfy a and b is a-5b=0a−5b=0
Step-by-step explanation:
Given : Equation 2x-3y=72x−3y=7 and (a+b)x-(a+b-3)y=4a+b(a+b)x−(a+b−3)y=4a+b represent coincident lines.
To find : Then a and b satisfy the equation ?
Solution :
When lines are coincident then the condition of equation a_1x+b_1y=c_1 , a_2x+b_2y=c_2a
1
x+b
1
y=c
1
,a
2
x+b
2
y=c
2
is
\frac{a_1}{a_2}=\frac{b_1}{b_2}=\frac{c_1}{c_2}
a
2
a
1
=
b
2
b
1
=
c
2
c
1
On comparing, The equation form is
\frac{2}{a+b}=\frac{3}{a+b-3}=\frac{7}{4a+b}
a+b
2
=
a+b−3
3
=
4a+b
7
Now, we can equate any two equation
\frac{2}{a+b}=\frac{7}{4a+b}
a+b
2
=
4a+b
7
Cross multiply,
2(4a+b)=7(a+b)2(4a+b)=7(a+b)
8a+2b=7a+7b8a+2b=7a+7b
8a-7a=7b-2b8a−7a=7b−2b
a=5ba=5b
a-5b=0a−5b=0
Therefore, The required equation satisfy a and b is a-5b=0a−5b=0
Step-by-step explanation:
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Answer
a-5b=0
Explanation
a+b/ 2 =a+b-3/3=4a+b/7
⇒a+b/2=4a+b/7
⇒7 (a + b) = 2(4a + b) (cross multiply)
⇒7a+7b= 8a + 2b
→ 8a-7a+2b-7b=0
⇒a-5b=0