#### 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; x^{2} + xy = -12**ii.** x^{2} + y^{2} = 29; x + y = 7**iii.** x + y = 5; x^{2} – 2y^{2} = 1**iv.** y – 5x = 3; x^{2} – y^{2} = -45 ** (WAEC)**

**i. **2x + y = 4; Â Â Â x^{2} + xy = -12

**Solution:**

**(i)** Let

x^{2} + xy = -12 â€¦â€¦â€¦.**(i)**

2x + y = 4 â€¦â€¦â€¦..**(ii)**

**Re-write as **

y = 4 – 2x â€¦â€¦â€¦â€¦.**(iii)**

**Substitute for y in equation (i) **

x^{2} + x(4 – 2x) = -12

**Expand brackets**

â‡’ x^{2} + 4x – 2x^{2} = -12

â‡’ x^{2} – 2x^{2} + 4x + 12 = 0

â‡’ -x^{2} + 4x + 12 = 0

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