# simultaneous equations??

- 0 votes

Im really confused! I don't how you know what to sub in etc and how to do them really. please help:-)

## 3 Answers

- 2 votes

Ok so

Example 1

3x+y=10......A

2x+y=7........B

(As the y's are the same, you can minus B from A)

A-B: 3x-2x=10-7

x=3

(If you then substitute x=3 into one of the equations, you can work out y)

Sub x=3 into A,

3*3+y=10

9+y=10

y=10-9

y=1

so x=3 and y=1.

Example 2

3x+2y=8......A

5x+6y=16.....B

(As none of the terms are the same, you must make them the same by multiplying the equation out)

A*3: 9x+6y=24....C

C-B: 4x=8

x=2

Sub x=2 into A

3*2+2y=8

6+2y=8

2y=2

y=1

so x=2 and y=1

Example 3

3x+2y=7......A

2x+5y=12.....B

(3 and 2 have a common multiple of 6)

A*2: 6x+4y=14......C

B*3: 6x+15y=36.....D

D-C: 11y=22

y=2

Sub y=2 into A,

3x+2*2=7

3x+4=7

3x=3

x=1

so x=1 and y=2

Example 4

4x-2y=18....A

3x-y=15......B

B*2: 6x-2y=30....C

(As both like terms are negative)

C-A: 2x=12

x=6

Sub x=6 into B

3*6-y=15

18-y=15

-y=-3

y=3

Example 5

2x-3y=0......A

3x+y=-11....B

B*3: 9x+3y=-33....C

(As like terms have different signs (- or +))

A+C: 11x=-33

x=-3

Sub x=-3 into B,

3*(-3)+y=-11

-9+y-11

y=-11+9

y=-2

so x=-3 and y=-2

Hope this has helped. If you want more examples, just ask. :)

Note: You do not have to include the stuff in brackets in your working.

- 1 vote

If you had:

3x + 2y = 8

2x + 5y = -2

Then get the y values to be the same - times the first equation by 5 and the second by 2:

15x + 10y = 40

4x + 10y = -4

Then take away as the signs are the same (positive 10y and positive 10y)

11x = 44 (40--4 = 40+4 = 44)

44/11 = 4

x = 4

Now you substitute x = 4 into the first equation:

3x + 2y = 8

(3x4) + 2y = 8

12 + 2y = 8

2y = 8 - 12

2y = -4

y = -4/2

y = -2

Then check this by substituting y = -2 and x = 4 into the second equation:

2x + 5y = -2

(2x4) + (5x-2) = -2

8+ -10 = -2

Hope this helps =) This is for the elimination method where you get rid of one of the unknowns.

For the substitution method you just substitute e.g. an x value into the other equation like this:

x = 4

2x + 5y = 20

Substitute x = 4 into it:

2(4) + 5y = 20

8 + 5y = 20

5y = 12

y = 2.4

Hope this wasn't too confusing! And if I've made any errors forgive me :)