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