Solve the pair of equations:
2/x + 3/y = 13
5/x - 4/y = -2

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 2/x + 3/ y = 13 can be expressed 2(1 /x) + 3(1/ y) = 13 be equation(1)

The equation 5/x - 4/y = -2 can be expressed 5(1/x) - 4(1/ y) = - 2 be equation (2)

Let 1/ x be a and 1/y be b.

⇒ 2a + 3b = 13 be equation (3)

⇒ 5a - 4b = - 2 be equation (4).

Let us use the elimination method to find the values of a and b.

Multiply equation (3) by 5 and equation (4) by 2

⇒ 10a + 15b = 65 be equation (5)

⇒ 10a - 8b = - 4 be equation (6)

Subtract equation (6) from equation (5)

⇒ (10a + 15b = 65 ) - (10a - 8b = - 4)

⇒ 23b = 69

⇒ b = 69/ 23 ⇒ b = 3

Substitute the value of b = 3 in equation (3)

⇒ 2a + 3(3) = 13

⇒ 2a + 13 - 9

⇒ 2a = 4 ⇒ a = 2

∵ a = 2; b = 3

∴ the value of x = ½; y = ⅓

Solve the pair of equations: 2/x + 3/y = 13, 5/x - 4/y = -2

Summary:

The values of x and y for the pair of linear equations is ½ and ⅓ which satisfies the equation

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