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Simultaneous Equations What are simultaneou s equations 30 April, 2017 Let me explain. If you have an equation like: x + y = 5, there are lots of answers. Here are some of these answers x+y=5 x+y=5 x+y=5 x+y=5 x=4 y=1 4+1=5 x=3 y=2 3+2=5 x=2 y=3 2+3=5 x=1 y=4 1+4=5 I can think of some more because 1.5 + 3.5 = 5 so x = 1.5 and y = 3.5 etc. There are lots of answers that fit the equation x + y =5 That’s right but suppose that we have another equation to go with x + y = 5 and the x and y must be the same numbers for both equations. x+y=5 Like this x–y=1 x+y=5 x–y=1 3+2=5 3–2=1 The only values that will fit both equations are x = 3 and y = 2. Equations like this are called simultaneous equations. x+y=9 x–y=5 Here is a method for solving simultaneous equations 1. Make sure that the middles are the same y y x+y=9 x–y=5 Here is a method for solving simultaneous equations 1. Make sure that the middles are the same 2. If the signs are different ADD (+ y) and (– y) have different signs so ADD x+y=9 x–y=5 2x = 14 Here is a method for solving simultaneous equations 1. Make sure that the middles are the same 2. If the signs are different ADD x + x = 2x and (+ y ) + (- y ) = 0 and 9 + 5 = 14 x+y=9 x–y=5 2x = 14 x=7 Here is a method for solving simultaneous equations 1. Make sure that the middles are the same 2. If the signs are different ADD 3. Find the value of x 2 x = 14 x = 14 ÷ 2 x=7 x+y=9 x–y=5 2x = 14 x=7 x+y=9 7+y=9 y=9–7 y=2 Here is a method for solving simultaneous equations 1. Make sure that the middles are the same 2. If the signs are different ADD 3. Find the value of x 4. Use this to find the value of y 7+y=9 y=9–7 y=2 Here is another pair of simultaneous equations 2x + y = 11 x–y=4 To solve, follow the steps 2x + y = 11 x–y= 4 3x = 15 1. Make sure that the middles are the same 2. If the signs are different ADD 2x + x = 3x (+ y) + (– y ) = 0 11 + 4 = 15 2x + y = 11 x–y= 4 3x = 15 x=5 1. Make sure that the middles are the same 2. If the signs are different ADD 3. Find the value of x 3x = 15 x = 15 ÷ 3 x=5 2x + y = 11 x–y=4 3x = 15 x=5 2x + y = 11 10 + y = 11 1. Make sure that the middles are the same 2. If the signs are different ADD 3. Find the value of x 4. Use this to find the value of y 2x + y = 11 x–y=4 3x = 15 x=5 2x + y = 11 10 + y = 11 y = 11 – 10 y=1 1. Make sure that the middles are the same 2. If the signs are different ADD 3. Find the value of x 4. Use this to find the value of y When the middle signs are the same 2x + y = 14 x+y=4 The same 2x + y = 14 x+y =9 x =5 2x + y = 14 10 + y = 14 y = 14 – 10 y=4 1. Make sure that the middles are the same 2. If the signs are the same SUBTRACT 3. Find the value of x 4. Use this to find the value of y 1. Make sure that the middles are the same 2. If the signs are the Same SUBTRACT If the signs are Different ADD 3. Find the value of x 4. Use this to find the value of y