Maths, Physics Revision Physicss Maths Physics Physics A Level Physics Home Maths Maths Revision hut Simultaneous Equations 1,Solving simultaneous equations using the graphical method Take the two equations  2x + 2y =10                                and  4x - 2y = 8 consider equation 2x + 2y =10  when x = 0,   2y = 10, so y = 5  the line crosses the Y axis at y=5 when y = 0, 2x = 10, so x=5 the line crosses the X axis at x = 5 consider equation 4x - 2y = 8 when x =0, - 2y = 8, so y = - 4 the line crosses the Y axis at y = - 4 when y = 0, 4x = 8, x=2 the line crosses the X axis at x=2 The values of x and y are  where the lines cross Play the animation Simultaneous equations are two equations both with two unknowns in them. You cannot  find the unknowns using one equation, you have to use them both. You can use either  of the following methods 2,Solving simultaneous equations using the elimination method Look at these two equations                                                                (1)          4x  + y  = 11                                               And        (2)          2x  + y  =  7 Subtract equation (2)  from equation (1) 2x + 0 = 4 2x = 4 x= 2 Substitute this value back into equation (1) + y = 11 y =3 Check answer in equation (2) 4 + 3 =7  Correct If one of the unknowns have different signs (1)      4x - y = 4 (2)    x + y =6 This time add equation (1)  to equation (2) 5x  +0 = 10 x = 2 (-y +y = 0) Substitute this value back into equation (1) 8 - y = 4 y = 4 Check the answer in equation (2) 2 + 4 =6  correct So x = 2 and y = 3 So  x = 2 and y = 4 If the unknowns have different values (1)      2x +y = 8 (2)    x + 2y = 7 Multiply equation (1) by 2 (3)    4x + 2y = 16 Subtract (2) from (3) 3x + 0 =9 x= 3 Substitute in equation (1) 6 + y = 8 y=2 Check the answer in (2) 3 + 4 = 7 correct So x = 3, y = 2 Sometimes you need to multiply both equations (1)     4x + 2y  = 20 (2)    2x  + 3y = 14 Multiply (1) by 3 (3)     12x + 6y  = 60 Multiply (2) by 2 (4)     4x + 6y =  28 Subtract (4) from (3) 8x + 0 = 32 x = 4 Substitute in equation 1 16 + 2y = 20 y = 2 Check answer in (2) 8 + 6 = 14  correct So x = 4, y = 2 And different signs (1)     2x + 3y = 16 (2)     3x - 4y  = 7 Multiply  (1) by 4 (3)     8x + 12y = 64 Multiply (2) by 3 (4)     9x  -12y = 21 Add (3) and (4) 17x +0 = 85 x= 5 Substitute in (1) 10 + 3y = 16 y = 2 Check answer in (2) 15 - 8 = 7  correct So x= 5, y = 2 top Click here for