## Advanced Simultaneous Equations answers

**Workout**

Question 1

(a) x = -5 and y = -2, x = 1 and y = 4

(b) x = -3 and y = -8, x = 3 and y = -2

(c) x = 1 and y = 1, x = 3 and y = 5

(d) x = -4 and y = -3, x = 1 and y = 12

(e) x = -4 and y = 29, x = -2 and y = 7

(f) x = -0.5 and y = -0.75, x = 2 and y = 8

Question 2

(a) x = -5 and y = 9, x = 1 and y = 3

(b) x = 2 and y = 5, x = 5 and y = 2

(c) x = 2 and y = 3, x = 3 and y = 2

(d) x = -2 and y = 0, x = 3 and y = 10

(e) x = -5 and y = -2, x = -2 and y = -5

(f) x = -6 and y = 1, x = 2 and y = -3

(g) x = 6 and y = 21, x = 7 and y = 31

(h) x = -0.6 and y = 0.8, x = 1 and y = 0

(i) x = -2 and y = 15, x = 4 and y = -15

(j) x = -0.3333… and y = 0.3333…

(k) x = 1 and y = 3, x = 2.333.. and y = 0.333…

(l) x = -9 and y = -2, x = 23 and y = 6

Question 3

(a) x = 3 and y = 1, x = 6.333… and y = -5.666..

(b) x = -4.284 and y = -1.284, x = 1.284 and y = 4.284

(c) x = -0.2915 and y = -0.2915, x = 10.2915 and y = 10.2915

(d) x = 1.14 and y = -2.72, x = 2.19 and y = -0.613

(e) x = -4.46 and y = 8.42, x = 1.46 and y = -3.42

(f) x = -4.46 and y = -6.46, x = 2.46 and y = 0.46

**Apply**

Question 1: (-3, 6) and (6, -3)

Question 2: 2 points of intersection and they are (-2, -10) and (2, -6)

Question 3: The distance is √8 (or 2.8284) as the points are (-2, 2) and (0, 4)

Question 4: (-3, 8) and (9/5, 176/25)

Question 5: (2, 7) as only one solution, it is tangent

Question 6: A and B are the points (2.25, -1.5) and (4, 2). Since the gradient of AB is 2 and the gradient of BC is -1/2, the lines are perpendicular. Therefore ABC is a right angled triangle.