Simultanoeus equations are when there are two equations, for example y = x+3 and y = x²+2x+1. As they are both 'y = ', x+3 = x²+2x+1 => x²+x-2=0 => (x+2)(x-1) = 0 => x=-2 or x=1. Substituing the values back into y = x+3, the y values are 1 and 4, giving coordinates of (-2,1) and (1,4).
There may be also questions where the equations may have a coefficent in front of the y. In that case, multiply the other y coefficent by that value so they btoh equal each other.
When given a linear inequality question, for example 3x+5 ≤ 4x+7, treat it as if it's a regular question, for example rearrange it to get -x-2 ≤ 0 => -x ≤ 2. Now, be careful when dividing or multiplying by a negative number, as you have to flip the sign to get x ≥ -2.
Quadratic inequalities are solved similarly to linear inequalities, but differ slightly. Take the equation 2x²+x ≥ 6. It can be rearranged to 2x²+x-6 ≥ 0. This can then be factorised to get (2x-3)(x+2) ≥ 0. Next, the best way to go on is to sketch the graph, as shown:
The picture shows that where the function is greater than 0, and so what values x could be (highlighted in blue). Solving the two linear inequalities show that x ≤ -2 or x ≥ 3/2. On other other hand, if the original function was less then 0, x would lie between -2 and 3/2 inclusive.