Simultaneous Equations

Question 0

Yr 8 example:
x + 5y = 11
x + 4y = 10

Answer 0

Subtract
Y = 1
Substitute
x + (5 x 1) = 11
x = 6

Question 1

Yr 8 example:
Solve
2x + y = 21
x - y = 6

Answer 1

Add them up in order to get rid of one of the letters
3x = 27
x = 9
Substitute
9-y = 6
y = 3

Question 2

Yr 9 example:
3x + 2y = 16
2x + y = 9
Times the second one by two

Answer 2

3x + 2y = 16
4x + 2y = 9 
Subtract 
x = 2 
Substitute 
4 + y = 9
y = 5

Question 3

Yr 9 example:
Solve 
2x + 5y = 16
3x + 4y = 17
Times both by three

Answer 3

6x + 15y = 48
6x + 8y = 34
Subtract
7y = 14
y = 2
Substitute
2x + 10 = 16
2x = 6
x = 3

Question 4

The substitution method
y = 6x -1
y = 4x + 15

Answer 4

4x + 15 = 6x - 1
16 = 2x
x = 8 
Substitute into any of the original equations
y = 32 + 15
y = 47

Question 5

Substitution method
y = 8 - 2x
3x - 2y = 5

Answer 5

3x - 2(8 - 2x) = 5
3x - 16 + 4x = 5 
7x = 21
x = 3 
Substitute 
y = 8 - (2 x 3) 
y = 8 - 6
y = 2

Question 6

Substitution method 
3x - 4y = 1 
y - 2x = 1 
Rearrange
3x - 4y = 1
y = 1 + 2x

Answer 6

3x - 4(1 + 2x) = 1 
3x - 4 - 8x = 1
-5x - 4 = 1
-5x = 5
-x = 1
x = -1
Substitute
y - 2 (-1) = 1
y + 2 = 1
y = -1

Question 7

Quadratic simultaneous equation
Find the intersection of
The curve: y = x(sq) + 2x - 4
And the line = x + 2

Answer 7

1) substitute
x + 2 = x(sq) + 2x - 4
2) simplify
0 = x(sq) + 2x - 4 - x - 2
0 = x(sq) + x - 6
3) solve the quadratic (factorise)
0 = x(sq) + x - 6 
0 = (x + 3) (x - 2)
x = -3 / x = 2 << first answer 
4) substitute the x value to get the y value 
y = x + 2 << the easier equation
FINAL ANSWER:
x = -3 / x = 2
y = -1 / y = 4