Simultaneous Equations – One Linear & One Quadratic

A linear equation is an equation that does not contain any powers higher than 1.

A quadratic equation is an equation with the highest power of 2.

Example 8.2.1:

Solve the following simultaneous equations:

i. 2x + y = 4;       x² + xy = -12
ii. x² + y² = 29;    x + y = 7
iii. x + y = 5;           x² – 2y² = 1
iv. y – 5x = 3;          x² – y² = -45                    (WAEC)

i. 2x + y = 4;       x² + xy = -12

Solution:

(i) Let 

x² + xy = -12  ……….(i)

2x + y = 4 ………..(ii)

Re-write as

y = 4 – 2x    ………….(iii)

Substitute for y in equation (i) 

x² + x(4 – 2x) = -12     

Expand brackets

⇒ x² + 4x – 2x² = -12

⇒ x² – 2x² + 4x + 12 = 0

⇒ -x² + 4x + 12 = 0