Solve the simultaneous equations - x+y=2 and 4y^2 - x^2 = 11

The objective of simultaeous equations is to be able to work out two unknowns by using two equations in which they are both involved. The first step is to label the equation x+y=2 as equation 1 and 4y² - x² = 11 as equation 2. Rearrange equation 1 to make one of the unknowns the subject so that we can susbititute this into the second equation leaving only one unknown for us to work out. For example, making x the subject gives us x=2-y and let that be equation 3. Now substitute this into equation 3 giving us the fourth equation 4y² - (2-y)² = 11. Expand the brackets giving us 4y² - (4-4y+y²) = 11 and then further simplify this to give us 3y² + 4y - 4 = 11. Now subtract 11 from both sides giving us the final quadratic 3y² + 4y - 15 = 0. Then use the product and sum method of factorising quadratics in order to factorise this equation to (y+3)(3y-5)=0. When the product of two things is zero, it must mean that one of the values equals zero so knowing this means that we know either y+3=0 or 3y-5=0 and so rearranging both gives us that y=-3 or y=5/3. We now use both values of y and substitute them back into equation 3 which is x=2-y to find out both values of x. This gives us x=5 (x=2--3) when y= -3 and x = 1/3 (x=2-5/3) when y= 5/3.