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Pair Of Linear Equations In Two Variables
Question
For which values of p does the pair of equations given below has unique solution?
Views: 840
Solution: For a pair of equations to have unique solutions,
Here,
So,
So, above pair equations has a unique solutions for all valuesof .
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Given, pair of linear equations is
2x + 3y – 5 = 0
px – 6y – 8 = 0
On comparing with ax + by + c = 0 we get
Here, a1 = 2, b1 = 3, c1 = – 5;
And a2 = p, b2 = – 6, c2 = – 8;
a1 /a2 = 2/p
b1 /b2 = – 3/6 = – ½
c1 /c2 = 5/8
Since, the pair of linear equations has a unique solution.
a1/a2 ≠ b1/b2
so 2/p ≠ – ½
p ≠ – 4
Hence, the pair of linear equations has a unique solution for all values of p except – 4.
Solution:
In the above equation a1= 4, a2 = 2, b1 = p and b2 = 2.
If the solution of a pair of linear equations is unique, then
a1/a2 ≠ b1/b2
4/2 ≠ p/ 2
Thus, the pair of linear equations has a unique solution for all values of p except 4
☛ Check: NCERT Solutions for Class 10 Maths Chapter 3
For which values of p does the pair of equations given below has unique solution? 4x + py + 8 = 0, 2x + 2y + 2 = 0
Summary:
The pair of linear equations has a unique solution for all the values of p except 4
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Solution : For a pair of equations to have unique solutions,
`a_1/a_2 != b_1/b_2`
Here, `a_1 = 4,a_2=2,b_1=p and b_2 = 2`
So,
`4/2!=p/2=>p!=4`
So, above pair equations has a unique solutions for all valuesof `p` `except` `4`.
\[\frac{a1}{a2}\] ≠ \[\frac{b1}{b2}\] is the condition for the given pair of equations to have unique solution.
\[\frac{4}{2}\] ≠ \[\frac{p}{2}\]
p ≠ 4
Therefore, for all real values of p except 4, the given pair of equations will have a unique solution.
Example 15 - Chapter 3 Class 10 Pair of Linear Equations in Two Variables [Term 1]
Last updated at Dec. 18, 2020 by
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Transcript
Example 15 For which values of p does the pair of equations given below has unique solution? 4x + py + 8 =0 2x + 2y + 2 = 0 4x + py + 8 = 0 2x + 2y + 2 = 0 4x + py + 8 = 0 Comparing with a1x + b1y + c1 = 0 ∴ a1 = 4 , b1 = p , c1 = 8 2x + 2y + 2 = 0 Comparing with a2x + b2y + c2 = 0 ∴ a2 = 2 , b2 = 2 , c2 = 2 So, a1 = 4 , b1 = p , c1 = 8 & a2 = 2 , b2 = 2 , c2 = 2 Since equations has unique number of solutions 𝒂𝟏/𝒂𝟐 ≠ 𝒃𝟏/𝒃𝟐 4/2 ≠ 𝑝/2 𝑝/2 "≠" 4/2 p "≠" 𝟒 So, for all values of p except 4, We will have a unique solution for the given set of questions