1. AS 3.15 Simultaneous Equations Starters
2 variables A Ans
2 variables B Ans
Introduce 3D planes C Ans
3D plane practice D Ans
Solving 3D Simultaneous E Ans
Solving with negatives F Ans
Solving with rearrangement G Ans
An Application H Ans
Another Application I Ans
Consistent Situations J Ans
More Consistency K Ans
Inconsistent L Ans
More Inconsistent M Ans

2. Simultaneous Eqns A Sketch the graphs of Y = 2x – 4 y = -0.5x + 6
Where do the two lines
intersect?
4) Write an equation of a
line parallel to line 1)

3. Simultaneous Eqns A ans
Sketch the graphs of
Y = 2x – 4
y = -0.5x + 6
Where do the two lines
intersect?
4) Write an equation of a
line parallel to line 1)

4. Simultaneous Eqns B Solve simultaneous equations y = 2x – 4
2) x + 3y = 18
x – 2y = -5
Find the ‘x’ and the ‘y’ intercepts of the equations in question 2) above
Rearrange the equations in Q 1) above to be in the form ax + by = c

5. Simultaneous Eqns B ans
Solve simultaneous equations
y = 2x – 4
y = -0.5x + 6
2) x + 3y = 18
x – 2y = -5
Find the ‘x’ and the ‘y’ intercepts of the equations in question 2) above
Rearrange the equations in Q 1) above to be in the form ax + by = c

6. Simultaneous Eqns C
Given two equations with two variables, explain geometrically the three possible situations that can
(in a 3D situation) Describe the plane z = 3
(in a 3D situation) Describe the plane x = -5
Find the three axis intercepts for the plane
2x + 3y – z = 12
Sketch the plane (in 3D) x + 2y = 8

7. Simultaneous Eqns C ans
Given two equations with two variables, explain geometrically the three possible situations that can
(in a 3D situation) Describe the plane z = 3
(in a 3D situation) Describe the plane x = -5
Find the three axis intercepts for the plane
2x + 3y – z = 12
Sketch the plane (in 3D) x + 2y = 8

8. Simultaneous Eqns D 1) Find the three axis intercepts for the plane
x + 2y + 3z = 9
Write an equation for a plane parallel to the plane in 1)
3) Find the three axis intercepts for the plane
x – 4z = 20
4) What effect would changing the coefficient of ‘y’ have on the plane in question 1? (From 2y to 9y)
5) Find the three axis intercepts for the plane
3x + 15 = 2y

9. Simultaneous Eqns D ans
1) Find the three axis intercepts for the plane
x + 2y + 3z = 9
Write an equation for a plane parallel to the plane in 1)
3) Find the three axis intercepts for the plane
x – 4z = 20
4) What effect would changing the coefficient of ‘y’ have on the plane in question 1? (From 2y to 9y)
5) Find the three axis intercepts for the plane
3x + 15 = 2y

10. Simultaneous Eqns E 1) Solve these simultaneous Equations
x + 2y – z = 2
x + y + z = 6
2x + y – z = 1
Write an equation for a plane parallel to the first plane above
Find the three intercepts to the first equation above

11. Simultaneous Eqns E ans
1) Solve these simultaneous Equations
x + 2y – z = 2
x + y + z = 6
2x + y – z = 1
Write an equation for a plane parallel to the first plane above
Find the three intercepts to the first equation above

12. Simultaneous Eqns F 1) Solve these simultaneous Equations
3x – 2y – 2z = -6
4x – y – 2z = -1
3x + 4y + z = 21
Write a different equation for a plane identical to the first plane above.
Describe geometrically what is happening in Question 1

13. Simultaneous Eqns F ans
1) Solve these simultaneous Equations
3x – 2y – 2z = -6
4x – y – 2z = -1
3x + 4y + z = 21
Write a different equation for a plane identical to the first plane above.
Describe geometrically what is happening in Question 1

14. Simultaneous Eqns G 1) Solve these simultaneous Equations
x = y + z + 4
2x + 4y = z
x + y = 5
Write an equation for a plane parallel to the second plane above.
Describe features of the plane formed by the first equation above.

15. Simultaneous Eqns G ans
1) Solve these simultaneous Equations
x = y + z + 4
2x + 4y = z
x + y = 5
Write an equation for a plane parallel to the second plane above.
Describe features of the plane formed by the first equation above.

16. Simultaneous Eqns H
By some miracle, Zoe can achieve her daily brain endorphin hit by solving three different types of mathematical problems: algebra, binary, and calculus
Each algebra problem takes 1 hour to do, involves 1 session of tears, and fills 2 pages in her book
Each binary problem takes 3 hours to do, involves 1 session of tears, and fills 1 page in her book
Each calculus problem takes 2 hours to do, also involves 1 session of tears, and fills 4 pages in her book
One eventful evening she spends 8 hours on maths problems, has only 4 sessions of tears, and fills 11 pages in her book.
How many of each type of problem did she do? (at Achieve level, cos the Merit is like this problem – too hard)

17. Simultaneous Eqns H ans
How many of each type of problem did she do?

18. Simultaneous Eqns I
Riley over-stepped the mark on yesterdays starter problem, so as punishment had to do exactly 80 press-ups, make up 68 worksheets and 24 starter problems of an acceptable standard.
On a school day he could do 1 press-ups, 2 work sheets and 1 starter problem.
On a weekend day he could do 2 press-ups, 3 work sheets and 1 starter problem.
On a holiday day he could do 5 press-ups, 3 work sheets and 1 starter problem.
How many weekend days will Riley need to be punished for?

19. Simultaneous Eqns I ans
How many weekend days will Riley need to be punished for?
Press-ups 1Sc + 2w + 5h = 80
Worksheets 2Sc + 3w + 3h = 68
Starters 1Sc + 1w + 1h = 24

20. Simultaneous Eqns J
1) Draw and explain all the situations where 3 variable simultaneous are ‘consistent’ - ie have solution(s)
Write down a set of 3 variable simultaneous equations that could give each of the situations above

21. Simultaneous Eqns J ans
1) Draw and explain all the situations where 3 variable simultaneous are ‘consistent’ - ie have solution(s)
Write down a set of 3 variable simultaneous equations that could give each of the situations above

22. Simultaneous Eqns K Solve this system of equations: 4x + 3y + 4z = 29
2x = 3z
3x + z = 5 + 2y
Given that this system of equations
x + 2y – z = 2
x + y + z = 6 ?
Form a third equation to make a system with infinite solutions
3) Form another third equation to make a different situation that has infinite solutions possible

23. Simultaneous Eqns K ans
Solve this system of equations:
4x + 3y + 4z = 29
2x = 3z
3x + z = 5 + 2y
Given that this system of equations
x + 2y – z = 2
x + y + z = 6 ?
Form a third equation to make a system with infinite solutions
3) Form another third equation to make a different situation that has infinite solutions possible

24. Simultaneous Eqns L
1) Draw and explain all the situations where 3 variable simultaneous are ‘inconsistent’ - ie have NO solutions
Write down a set of 3 variable simultaneous equations that could give each of the situations above

25. Simultaneous Eqns L ans
1) Draw and explain all the situations where 3 variable simultaneous are ‘inconsistent’ - ie have NO solutions
Write down a set of 3 variable simultaneous equations that could give each of the situations above

26. Simultaneous Eqns M Solve this system of equations: x + 3y + 2 = 3z
3x + 3 = 3z
Given that this system of equations
x + 2y – z = 2
2x + y + 3z = 1 ?
Form a third equation to make a system with NO solutions
3) Form another third equation to make a different situation that has NO solutions possible

27. Simultaneous Eqns M ans
Solve this system of equations:
x + 3y + 2 = 3z
2x + 3 = y + 2z
3x + 3 = 3z
Given that this system of equations
x + 2y – z = 2
2x + y + 3z = 1 ?
Form a third equation to make a system with NO solutions
3) Form another third equation to make a different situation that has NO solutions possible