Maths Unit 25 – Solving Equations Forming and solving equations from diagrams Forming and solving simultaneous equations 3b + f = £12 - b + f = £8 2b = £4 b = £2 Now we know the burger costs £2, you can work out how much a burger is by substituting the cost of the fries into one of the equations. 2b + f = £12 b + f = £8 b + f = £8 £2 + f = £8 f = £6 The idea is to eliminate one of the unknowns either by adding or subtracting the equations. Here we need to subtract. Remember to balance your equation by doing the same to both sides. -£2 -£2 Forming and solving equations from wordy problems Remember to balance your equation by doing the same to both sides. To solve a quadratic equation you need to factorise it n2 + 7n + 10 = 0 Now set bracket equal to zero and solve each equation. (n+2) = 0 so n = -2 and (n+5) = 0 so n = -5 These are the values which make the equation equal to zero. -8 -8 I think of a number. I multiply it by 3 and add 8. My answer is 23. What number did I first think of? ÷ 3 ÷ 3 Key word definitions Forming an equation – interpreting a problem or diagram and creating an equation which will help you solve the problem. Expression - in algebra this is a combination of terms Equation - a mathematical statement that has two things equal to each other. It consists of two expressions either side of an equals sign. Solve – to find the solution which is value or set of values which makes the equation work Linear equation – an equation with an unknown which does not have any powers. If the equation is graphed it would create a straight line. Quadratic equation – an equation which includes as least one term that is squared. A quadratic equation has the form of ax2 + bx + c = 0 where a, b and c are constant values and x is the unknown value. Simultaneous equations – equations involving two or more unknowns that are to have the same values in each equation Divisor – a number by which another number is divided by.