1. Module :MA0001NP Foundation Mathematics Lecture Week 9

2. Transposing formulae & Simultaneous equations

3. Transposing formulae…
What if we have the temperature in °C and what to convert it to °F ?
We need to transpose the formula to make F the subject…
C = (F – 32)
C = F – 32 So, C + 32 = F
Here the subject of the formula is changed from C to F

4. Transposition of Formulae
Changing the subject of a formula
e.g Formulae to find perimeter of rectangle
P = 2l + 2w
Rearrange the formula to make l the subject
= l + w
So w = l
Remember:
Whatever we do to one side we must do to the other side to maintain the equality

5. Transposition of Formulae
Rearrange the formula to make y the subject
3x + 2y = 7
2y = 7 – 3x
y = 7 – 3x 2
Subtract 3x from both sides
Divide both sides by 2

6. Transposition of Formulae
Transpose the formula to make the subject
a. C = 2∏r for r
b. Y – z = 3(x+2) for x
c. T = 2∏√(l/g) for l
d. x²+y² = 2 for y
e. A² = B² + 2SR for B

7. Simultaneous Equations & Intersections
As the y-values are the same, the right-hand sides of the equations must also be the same.
Two Lines At the point of intersection, we notice that the x-values on both lines are the same and the y-values are the same.
Substituting into one of the original equations, we can find y:
The point of intersection is

8. Simultaneous Equations & Intersections
1 quadratic equation and 1 linear equation
e.g.
This is a quadratic equation, so we get zero on one side and try to factorise:
To find the y-values, we use the linear equation, which in this example is equation (2)
The points of intersection are (1, 1) and (-3, 9)
Since the y-values are equal we can eliminate y by equating the right hand sides of the equations:

9. Simultaneous Equations & Intersections
e.g.
Sometimes we need to rearrange the linear equation before eliminating y
Rearranging (2) gives
Eliminating y: or
Substituting in (2a):

10. Simultaneous Equations & Intersections
Solving the equations simultaneously will not give any real solutions.
Special Cases
e.g. 1 Consider the following equations:
The line and the curve don’t meet.
The discriminant

11. Simultaneous Equations & Intersections
e.g. 2
Eliminate y:
The discriminant,
The quadratic equation has equal roots.
The line is a tangent to the curve.
Solving