Solve The System Of Second-degree Equation

Find the value of xy by solving the system of second-degree equation in two variables
Solve the second-degree equation x² + xy = 28 and y² + xy = 21 then find the value of xy
Solution
Let
x² + xy = 28…………….. equation 1
y² + xy = 21…………….. equation 2
Add equation 1 and equation 2 then
x² + xy + y² + xy = 28 + 21
⇒ x² + 2xy + y² = 49
⇒ (x + y)² = 49
⇒ x + y = ±7
Subtract equation 2 from equation 1, then
x² + xy – (y² + xy) = 28 – 21
⇒ x² – y² = 7
⇒ (x + y)(x – y) = 7
When x + y = 7
⇒ 7(x – y) = 7
⇒ x – y = 1
x + y + x – y = 7 + 1
⇒ 2x = 8
⇒ x = 4
y = x – 1 = 4 – 1 = 3
xy = 4 × 3 = 12
When x + y = -7
⇒ -7(x – y) = 7
⇒ x – y = -1
x + y + x – y = -7 – 1
⇒ x = -4
y = x – 1 = -4 + 1 = -3
xy = (-4) × (-3) = 12