Solve algebraically the simultaneous equations x^2 + y^2 = 25 and y − 2x = 5 (5 marks)
First consider each equation separately and label them with a number. x2 + y2 = 25 (1) y - 2x = 5 (2)This question is difficult as it involves square numbers, unlike a normal simultaneous equation. Hence why there are 5 marks for it. *A common mistake is to go straight into (1) and square root the whole thing to get like terms for (2). By doing that you are actually creating more problems than is needed as the square root of 25 can be +5 or -5 and the square root of x2 and y2 can be +/- x and y. So as you cannot square or square root equations and you cannot add or minus them (no 'like' terms), try and substitute. For instance, rearrange (2) like so: y = 2x + 5 And substitute (2) into (1): x2 + (2x+5)(2x+5) = 25Expand the brackets like normal and collect like terms: 5x2 + 20x = 0Factorise to get the x values: 5x(x +4) = 0Find the x values: x = 0 x = -4Find the y values by substituting x into (1) always remember to do thisy = 5 (when x=0) y= 3 (when x = -4)By writing out the method like this, you should obtain the three M1 marks even if you get the x and y values wrong by mistake.
