Solve the simultaneous equations: x+y=2 , 4y²-x²=11

These equations would best be solved using the substitution method, in this case the easiest way would be substituting x. For the first equation we need to rearrange it to get x on one side so we have x=2-y.So if we substitute x from the first equation into the second equation we get 4y² - (2-y)²=11. The next step is to solve this equation to find y. By expanding the brackets we get 4y²- 4+4y- y²=11. If we simplify this leads to the quadratic equation of 3y² + 4y- 15=0. We can factorise this to get (3y-5) (y+3)= 0. Therefore y= 5/3 or -3.If we substitute our values for y into equation 1 which is x+y=2, we get x= 2-5/3 and x= 2-(-3), therefore x= 1/3 or 5.So the final values are x= 1/3, y= 5/3 or x=5, y=-3.