What is the answer to this?

Question

(x)/(2)+(y)/(4)+(7)/(3)=24

(x)/(4)+(y)/(3)+(7)/(2)=29

(x)/(3)+(y)/(2)+(7)/(4)=25

Answer 1

We have 3 simultaneous equations in 2 variables x and y.

We can leave as fractions, but I think it's easier to do a bit of multiplication (I chose 6) to simplify.

(1) ^x/₂ + ^y/₄ + ⁷/₃ = 24 ≡ 3x + 1.5y + 14 = 144 ≡ 3x + 1.5y = 130

(2) ^x/₄ + ^y/₃ + ⁷/₂ = 29 ≡ 1.5x + 2y + 21 = 174 ≡ 1.5x + 2y = 153

(3) ^x/₃ + ^y/₂ + ⁷/₄ = 25 ≡ 2x + 3y + 10.5 = 150 ≡ 2x + 3y = 139.5

we need some combination of multiplication and addition/subtraction to eliminate either x or y.

(1) - 2 x (2) will eliminate x as follows:

3x + 1.5y = 130

-

3x + 4y = 306

=

0x - 2.5y = -176

=> 2.5y = 176

=> 5y = 352

=> y = 70.4 or 70 ²/₅

now we have y, substitute in (2) to get 1.5x + 2(70.4) = 153

=> 1.5x = 153 - 2(70.4) = 153 - 140.8 = 12.2

=> 3x = 24.4

=> x = 8 ²/₁₅

Let's double-check in one of the original equations:

^x/₂ + ^y/₄ + ⁷/₃ = 24

=> ( 8 ²/₁₅) /₂ + ^70.4/₄ + ⁷/₃ = 4 ¹/₁₅ + 17.6 + ⁷_/3 = 21.6 + 1/15 + 35/15

= 21.6 + 36/15 = 21.6 + 2 + 6/15 = 23.6 + 2/5 = 23.6 + 0.4 = 24 as required