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## SS2: MATHEMATICS - 2ND TERM

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Lesson 8, Topic 2
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# Simultaneous Equations – One Linear & One Quadratic

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#### Topic Content:

• 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

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1. This is very nice
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