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Solving harder linear Simultaneous Equations

7 x - 4 y = 37. 21 x - 12 y = 111. 2 x + 3 y = - 6. 8 x + 12 y = - 24. x 3. x 4. Substitute in . 2. 2. 1. 2. 1. 3. 4. 1. 4. 3. +. 29. 3. Check in . Solving harder linear Simultaneous Equations. In this case there is no single multiplier for one equation in order

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Solving harder linear Simultaneous Equations

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  1. 7x - 4y = 37 21x - 12y = 111 2x + 3y = -6 8x + 12y = -24 x 3 x 4 Substitute in 2 2 1 2 1 3 4 1 4 3 + 29 3 Check in Solving harder linear Simultaneous Equations In this case there is no single multiplier for one equation in order to make coefficients the same, so we have to multiply both equations Use the smallest possible multiplier to produce the smallest numbers To work with 29x = 87 x = 3 (2x 3) + 3y = -6 (7 x 3) - (4 x -4) = 37 3y = -12 -6 y = -4

  2. 3x - 2y = 6 5x - 3y = 9 10x - 6y = 18 x 3 x 2 9x - 6y = 18 Subtract - Substitute in 2 1 2 1 2 4 4 1 3 3 2 Check in Solving harder linear Simultaneous Equations Practice x = 0 (3x 0) - 2y = 6 -2y = 6 y = -3 (5 x 0) – (3 x-3) = 9

  3. Make x the subject of the formula because making y the subject would look like this and would be harder to substitute Solving non-linear Simultaneous Equations Solve the simultaneous equations: x2 + y2 = 13 x + 3y = 3 The way to solving these is to convert them into quadratic equations in the form ax2 + bx +c Step 1 Rearrange the linear equation because this will be used to substitute into the quadratic equation. x = 3 – 3y Step 2 Substitute x = 3 – 3y into thenon-linear equation (3 - y)2 + y2 = 13 Expand and simplify (9y2 -18y + 9) + y2 = 13

  4. x = x + 3 x = 3 When Solving non-linear Simultaneous Equations Step 3 10y2 -18y + 9 = 13 Rearrange to make the equation = 0 10y2 -18y - 4 = 0 Factorise and solve the quadratic equation Step 4 (5y+1)(y-2) = 0 y = 2 Substitute into the linear equation (easiest) Step 5 x = -3 x + 3 x 2 = 3 When y = 2 Check your answers by substitution into the non-linear equation

  5. Solving non-linear Simultaneous Equations Practice x2 + y2 = 16 y = x - 4 Substitute into the non-linear equation x2 + (x – 4)2 = 16 Expand and simplify x2 + (x2 - 8x + 16) = 16 2x2 - 8x + 16 = 16 Rearrange to make the equation = 0 2x2 - 8x = 0 x = 4 x = 0 2x(x – 4)= 0 Substitute into the linear equation Check the values in the non linear equation When x = 0, y = -4 When x = 4, y = 0

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