Aims: To be able to solve a pair of simultaneous linear equations using both the elimination and substitution methods To be able to set up a pair of simultaneous equation to solve. Co-ordinate Geometry Lesson 6 Linear simultaneous equations Linear simultaneous equations can be solved algebraically using: The substitution method. The elimination method, or When will a pair of linear simultaneous equations have no solutions? Solving a pair of simultaneous equations finds the point where the two lines intersect: The elimination method is probably the one you used for GCSE. Sometimes it is necessary to multiply one or both of the equations before we can eliminate one of the variables. Example 1 Solve:5 x 2 y = 31 4 x + 3 y = 11 The elimination method We need to have the same number in front of either the x or the y terms before adding or subtracting the equations x 6 y = x + 6 y = Substitute x = in So the solution is x =, y =. The elimination method y = 2 x 3 2 x + 3 y = 23 Example 2 Solve: The substitution method Two simultaneous equations can also be solved by substituting one equation into the other. For example: Substitute 1 into 2 : 1 2 Substituting x = 4 into 1 gives So the solution is x =, y =. The substitution method Rearrange equation 1 : 3 x y = 9 8 x + 5 y = Example 3 Solve: Now substitute y = into equation 2 : The substitution method Substitute x = into equation 1 to find the value of y : So the solution is x =, y =. Complete Puzzle Big Jim is 92kg heavier than Wee Jim. The sum of their weights is 236kg. What do they each weigh? Setting up and solving Simultaneous Equations Try on white boards Andrew and Doreen book in at the Sleepwell Hotel. Andrew stays for three nights and has breakfast on two mornings. His bill is 145. Doreen stays for five nights has breakfast on three mornings. Her bill is 240. Find the cost of one breakfast! I think that receptionist was checking me out! C The perimeter of the triangle is 42 cm. PR is 2cm longer than QR. Calculate the values of x,y. G