Equations and Inequalities
Linear Simultaneous Equations
Like in GCSE (used to find the meeting point of two straight lines)
Two equations can cancel out one of the constants by either adding or subtracting
x + 2y = 5 (1)
3x - 2y = 7 (2)
3x + 6y = 15 (1)
- - - minus all the values
3x - 2y = 7 (2)
0 + 8y = 8
y = 1
Two equations can cancel out one of the constants by either adding or subtracting
x + 2y = 5 (1)
3x - 2y = 7 (2)
3x + 6y = 15 (1)
- - - minus all the values
3x - 2y = 7 (2)
0 + 8y = 8
y = 1
Non-Linear Simultaneous Equations
This is when a quadratic needs to be resolved (used to find meeting point of a quadratic and a straight line)
This is done by substitution of either constant.
This is done by substitution of either constant.
Linear Inequalities
Treat < or > as an =
7 - 2x > 3 Always avoid division with negatives as this makes the sign flip
7 > 3 + 2x
4 > 2x
2 > x
7 - 2x > 3 Always avoid division with negatives as this makes the sign flip
7 > 3 + 2x
4 > 2x
2 > x
Quadratic Inequalities
Best solved when the quadratic is drawn
On the graph this means any value in the shaded regions complies with the inequality. If the sign was the opposite it would require the values below the x axis.