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 (i) - The difference between two numbers is 26 and one number is three times the other. Find them.
- Ex 3.2 Q3 (ii) - The larger of two supplementary angles exceeds the smaller by 18 degrees. Find them.
- Ex 3.2 Q3 (iii) - The coach of a cricket team buys 7 bats and 6 balls for ₹3800. Later, she buys 3 bats and 5 balls for ₹1750. Find the cost of each bat and each ball.
- Ex 3.2 Q3 (iv) - The taxi charges in a city consist of a fixed charge together with the charge for the distance covered. For a distance of 10 km, the charge paid is ₹105 and for a journey of 15 km, the charge paid is ₹155. What are the fixed charges and the charge per km? How much does a person have to pay for travelling a distance of 25 km?
- 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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