Solve the simultaneous equations y = 5x^2 + 4x - 19 and y = 4x + 1

Okay, so for two simultaneous equations which both equal the same variable (in this example the variable they're equal to is y), the trick is to make both equations equal each other:so we can say that 4x + 1 = 5x^2 + 4x - 19This is very useful, because now that our equation only has x's in it, we can put everything onto one side, and solve itNote: it's easier to solve positive quadratic equations, so we want to move the LHS onto the RHS1) minus the 4x and the 1 from both sidesthis gives us 5x^2 - 20 = 02) Here the equation is simply solvedwe then add the 20 to both sides and divide by 5 givingx^2 = 4we then take the square root of both sidesCAREFUL: When taking the square root of x^2 = 4, we must be aware that as well as getting x = 2, we get x = -2
3) So we have two x-values, there must be a y-value for eachso we sub in our x-values to either of the simultaneous equationsthe easiest one is y = 4x +1so when x = 2, y = (4x2) + 1 = 9and when x = -2, y = (4x-2) + 1 = -7