Solve the simultaneous equations x^2 + y^2 = 9 and x+ y = 2. Give your answer to 2.d.p
Label your two equations 1 and 2 respectively. Make x the subject of the second equation, so x=2-y. Substitute x=2-y into x^2+y^2=9, to give (2-y)^2+y^2=9. Expand the brackets using FOIL to give 4-4y+y^2+y^2=9. By grouping like terms together get 2y^2-4y-5=0. Because the question asks for the answer in 2.d.p, you know to use the quadratic formula, so substitute into the given formula where a=2, b=-4 and c=-5 (dont forget the minus sign!). Using the + and the - sign you get y=2.87 and y=-0.87. Then substitute these values into x+y=2 to get x=-0.87 and x=2.87.
GS
Related Maths GCSE answers
All answers ▸There are N counters in a bag, 4 being red and the rest being blue. I take two counters at random from the bag (without replacing the first).The chance i take two blue counters is 1/3, See below in the answer box
Given that x^2+10x+3 can be written in the form (x+a)^2+b, find the values of a and b.
There are 2 banks, Bank A and Bank B. Bank A provides compound interest of 1.3%. Bank B provides interest of 3.5% for the first year and then 0.7% for each extra year. James wants to invest £250. Which bank provides the most interest after 4 years?
Two points P(–4, –1) and Q(–8, 5) are joined by a straight line. Work out the coordinates of the midpoint of the line PQ.