SOLVE THE FOLLOWING SIMULTANEOUS EQUATIONS: 5x^2 + 3x - 3y = 4, -4x - 6y + 5x^2 = -7
Question: 5x2 + 3x - 3y = 4, -4x - 6y + 5x2 = -7.........Step 1: make the y-coefficient equal in both equarions: (y and not x because it has the lowest power so it is easier, but x would also work)........ (5x2 + 3x - 3y) * 2 = (-4) * 2 . 10x2 + 6x - 6y = 8 ........Step 2: There are three ways of solving this. In this example, I will teach you equalizaton: Rearange so the y-terms in both equations are alone on one side: ........10x2 + 6x - 6y = 8 --> 10x2 + 6x - 8 = 6y............. -4x - 6y + 5x2 = -7 --> -4x + 5x2 + 7 = 6y........... Therefore, 6y = 10x2 + 6x - 8 = -4x + 5x2 + 7 ............Step 3: Now solve the new equation which contains only one variable: ........10x2 + 6x - 8 = 4x + 15x2 -5............ Move all terms to the left so f(x)=0:............ 10x2 + 6x - 8 = -4x + 5x2 + 7 --> 10x2 + 6x - 8 + 4x - 5x2 - 7 = 0 --> 5x2 + 10x - 15 = 0 --> x2 + 2x - 3 = 0 --> (x+3)(x-1) = 0 so x = 1, -3................ Step 4: Substitute x = 1 and x = -3 into either equation above:........... x = 1: 5x2 + 3x - 3y = 4 --> 5(1)2 + 3(1) - 3y = 4 --> 5 + 3 - 3y = 4. --> 3y = - 4 --> y = 4/3.................. x = -3: 5(-3)2 + 3(-3) - 3y = 4. --> 45 - 9 - 3y = 4. --> 3y = 32 --> y = 32/3
