Determinant methods cramers rule to solve the simultaneous

Question

1. Simplify the following completely

x- 3 / (x-1)(x-2) -  x-2/ (x-1) (x-3)

2. Solve for x if (10 - 2x)/6 + (2x -2)/3 = 2x - 4

3. Solve simultaneously; 2x + 3y = 10 and 3x - 2y = 2

4. Solve for x if = = 0

5. Use the determinant methods Cramer's rule to solve the simultaneous equations 2x - y = 1 and x+2y = 8

6. Let matrix A =  , find the determinant of A.

7. Solve for x; ¦5x +3¦> 2

8. Line a is joined by the points P (2, 2) and Q (5, 6). Find

(a) The length of a

(b) The mid-point of a

(c) The slope of a

9. Divide 3x³ + x² - 5 by x +4

10. Show that (x+2) is a factor of x +2x - x - 2 and hence find the other factors.

11. Simplify;

12. Shade the region satisfying the inequalities below;

x+2y ≤ 12,
x ≤ 8 ,
x+y ≥ 3
x ≥ 0
y ≥ 0