Ex 3.2 Q2 - Solve 2x + 3y = 11 and 2x - 4y = -24 and hence find the value of ‘m’ for which y = mx + 3.
Solution:-Given,
2x + 3y = 11 ----- ( 1 )
2x - 4y = -24 ----- ( 2 )
➙ From Eqⁿ(1)
2x + 3y = 11
∴ 2x = 11 - 3y
∴ x =
11 - 3y
/
2
➙ Putting x =
11 - 3y
/
2
in Eqⁿ(2) ∴ 2[
11 - 3y
/
2
] - 4y = -24 ∴ 11 - 3y - 4y = -24
∴ 11 - 7y = -24
∴ 7y = 24 + 11
∴ 7y = 35
∴ y =
35
/
7
∴ y = 5
➙ Putting y = 5 in Eqⁿ(1)
∴ 2x + 3(5) = 11
∴ 2x + 15 = 11
∴ 2x = 11 - 15
∴ 2x = -4
∴ x =
-4
/
2
∴ x = -2
➙ Given,
y = mx + 3
*Putting x = -2 & y = 5
∴ 5 = m(-2) + 3
∴ 5 = -2m + 3
∴ 2m = 3 - 5
∴ 2m = -2
∴ m =
-2
/
2
∴ m = -1
Hence,
The required value of m is -1.
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Try This..
✒ Solve: 3x + 2y = 12 and 2x - y = 1.
✒ Find the value of m: If (x = 1, y = 2) satisfies y = mx + 1, find m.
✒ Determine whether the following system is consistent or inconsistent: x + y = 6 and 2x + 2y = 12
❌ Common Mistakes
Sign errors while subtracting equations:▸ Always double-check when you subtract. A small sign error can give a wrong answer.Substituting wrong values:▸ After finding one variable, substitute carefully into the correct equation.Mixing up equations:▸ Label equations clearly as Eq(1), Eq(2), etc., to avoid confusion.Wrong rearrangement in m value step:▸ Rearranging y = mx + 3 incorrectly is a frequent mistake. Use the substitution method cleanly.
📝 Related Questions:-
- Ex 3.2 Q3 (v) - A fraction becomes 9/11, if 2 is added to both the numerator and the denominator. If, 3 is added to both the numerator and the denominator it becomes 5/6. Find the fraction.
- Ex 3.2 Q3 (vi) - Five years hence, the age of Jacob will be three times that of his son. Five years ago, Jacob’s age was seven times that of his son. What are their present ages?
Queries Solved:-
Class 10 Ex 3.2
Ex 3.2 Q2 Class 10
Class 10 Ex 3.2 Q2
Class 10 Chap 3 Ex 3.2 Q2
Class 10 Pair Of Linear Equations in Two Variables
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