Simultaneous Equations - Topic 7

Question 1

If signs are different :

If signs are same :

Answer 1

+

-

Question 2

X + y = 5

X - y = 3

Answer 2

X + y = 5
\+ x - y = 3
-------------
2x = 8
X = 4

X + y = 5
4 + y = 5
Y = 5 - 4
Y = 1

Question 3

The sum of 2 numbers is 21 and the difference is 7. What are the 2 numbers?

Answer 3

X + y = 21
\+ X - y = 7
------------
2x = 28
X = 14

X + y = 21
14 + y = 21
y = 21 - 14
Y = 7

The 2 numbers are 14 and 7.

Question 4

2x + y = 11

3x - 2y = 6

Answer 4

2x + y = 11 (x2)
+ 3x - 2y = 6

4x + 2y = 22
\+ 3x - 2y = 6
---------------
7x = 28
X = 4

2x + y = 11
8 + y = 11
Y = 11 - 8
Y = 3

Question 5

5x + 2y = 16

8x +2y = 11

Answer 5

8x + 2y = 22
- 5x + 2y = 16
-----------------
3x = 6
X = 2

5x + 2y = 16
10 + 2y = 16
2y = 16 - 10
2y = 6
Y = 3

Question 6

3x + 4y = 17

2x + 5y = 16

Answer 6

2x + 5y = 16 (x4)
3x + 4y = 17 (x5)

15x + 20y = 85
- 8x + 20y = 64
-------------------
7x = 21
X = 3

2x + 5y = 16
6 + 5y = 16
5y = 16 - 6
5y = 10
Y = 2

Question 7

4x + y = 15

3x + y = 8

Answer 7

4x + y = 15
- 3x + y = 8
————-
x = 7

4x + y = 15
28 + y = 15
Y = 15 - 28
Y = -13

Question 8

9x + 12y = -4

3x - 12 y = 12

Answer 8

9x + 12y = -4
\+ 3x - 12y = 12
-------------------
12x = 8
X = 8/12
X = 2/3

Question 9

2 hats + 3 caps = £55

5 hats + 2 caps = £88

Answer 9

2x + 3y = 55 (x2)
5x + 2y = 88 (x3)

15x + 6y = 264
- 4x + 6y = 110
----------------
11x = 154 
X = 14

2x + 3y = 55
28 + 3y = 55
3y = 55 - 28
3y = 27
Y = 9

Question 10

4x + y = 23

3x + y = 18

Answer 10

4x + y = 23
- 3x + y = 18
—————–
X = 5

4x + y = 23
4 (5) + y = 23
20 + y = 23
Y = 23 - 20
Y = 3