Solve the following pair of equations by reducing them to a pair of linear equations:
5 / (x -1) + 1 / (y - 2) = 2
6 / (x - 1) - 3 / (y - 2) = 1
Solution:
The standard form of a linear equation is ax + by + c = 0.
To reduce a pair of equations to the standard form, we will use substitution.
The equation 5/(x - 1) + 1/(y - 2) = 2 can be expressed 5(1 /x - 1) + 1(1/ y - 2) = 2 be equation(1)
The equation 6/(x - 1) - 3/(y - 2) = 1 can be expressed 6(1/x - 1) - 3(1/ y - 2) = 1 be equation (2)
Let 1/(x - 1) be a and 1/(y -2) be b.
⇒ 5a + b = 2 be equation (3)
⇒ 6a - 3b = 1 be equation (4).
Let us use the elimination method to find the values of a and b.
Multiply equation (3) by 3 and equation (4) by 1.
⇒ 15a + 3b = 6 be equation (5)
Add equation (4) and (5)
⇒ (15a + 3b = 6) + (6a - 3b = 1)
⇒ 21a = 7
⇒ a = ⅓
Substitute a = ⅓ in equation (3)
5(⅓) + b = 2
5 + 3b = 6
b = ⅓
∵ a = ⅓ ; b = ⅓
the value of x - 1 = 3; y - 2 = 3.
∴ x = 4; y = 5
☛ Check: NCERT Solutions for Class 10 Maths Chapter 3
Solve the following pair of equations by reducing them to a pair of linear equations: 5 / (x -1) + 1 / (y - 2) = 2, 6 / (x - 1) - 3 / (y - 2) = 1
Summary:
The values of x and y for the pair of linear equations is 4 and 5 which satisfies the equation
☛ Related Questions:
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