Question

Solve using the substitution method. 3x +2y= 19 xy= 15​

Answer 1

when x = 3 1/3, y = 4.5

or

when x =3 , y = 5

Explanation:

Here, we want to solve using substitution

xy = 15

let x = 15/y

Put this into the first equation;

3(15/y) + 2y = 19

45/y + 2y = 19

Multiply through by y

45 + 2y^2 = 19y

2y^2 -19y + 45 = 0

2y^2 - 10y - 9y + 45 = 0

2y(y-5) -9(y-5) = 0

(2y-9)(y-5) = 0

2y-9 = 0

or y-5 = 0

2y = 9 or y = 5

y = 9/2 or y = 5

y = 4.5 or y = 5

Recall;

x = 15/y

x = 15/4.5 or x = 15/5

x = 3 1/3 or x = 3