Chapter 1 Linear Systems 1. Solve each linear system. For each system, explain why you chose the method that you used. Check each solution. a) \( x+2 y=3 \) \( 3 x-y=1 \)

8. Factorise each of the following expressions. (a) \( x(x-5)+6 \) (b) \( x^{2}+3(x-6) \) (c) \( (x-3)^{2}+12 x \) (d) \( (x+3)(x-4)-8 \) (e) \( (3 x-4)(2 x-5)+8(2 x-5) \) (f) \( (3 x-4)^{2}-(2 x+1)^{2} \)

5. Factorise each of the following expressions by splitting the middle term. \( \begin{array}{ll}\text { (a) } x^{2}+3 x+2 & \text { (b) } x^{2}+5 x+6 \\ \text { (c) } y^{2}-7 y+10 & \text { (d) } y^{2}-8 y-9 \\ \text { (e) } z^{2}+2 z-3 & \text { (f) } z^{2}+14 z-15\end{array} \)

10. \( \frac{7 x+65}{5}=6 \)

6. Factorise each of the following expressions. \( \begin{array}{ll}\text { (a) } 2 x^{2}+3 x+1 & \text { (b) } 2 x^{2}+7 x+5 \\ \text { (c) } 3 y^{2}-5 y+2 & \text { (d) } 3 y^{2}-11 y+10 \\ \text { (e) } 4 m^{2}-4 m+1 & \text { (f) } 4 m^{2}+4 m-3\end{array} \)

56. Вычислите значение выраже \( \frac{\sqrt{5}+\sqrt{7}}{\sqrt{5}-\sqrt{7}}+\frac{\sqrt{5}-\sqrt{7}}{\sqrt{5}+\sqrt{7}} \).