Simultaneous Equations 8 January, 2016 What are simultaneou s equations Let me explain. If you have an equation like: x + y = 5, there are lots of answers.

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Simultaneous Equations 8 January, 2016 What are simultaneou s equations 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 = 4y = = 5 x + y = 5 x = 3y = = 5 x + y = 5 x = 2y = = 5 x + y = 5 x = 1y = = 5 I can think of some more because = 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 x – y = 1 Like this

The only values that will fit both equations are x = 3 and y = 2. Equations like this are called simultaneous equations. x + y = 5 x – y = = 5 3 – 2 = 1

Here is a method for solving simultaneous equations x + y = 9 x – y = 5 1.Make sure that the middles are the same y

Here is a method for solving simultaneous equations x + y = 9 x – y = 5 1.Make sure that the middles are the same 2.If the signs are different ADD (+ y) and (– y) have different signs so ADD

Here is a method for solving simultaneous equations x + y = 9 x – y = 5 2x = 14 1.Make sure that the middles are the same 2.If the signs are different ADD x + x = 2x and (+ y ) + (- y ) = 0 and = 14

Here is a method for solving simultaneous equations x + y = 9 x – y = 5 2x = 14 x = 7 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

Here is a method for solving simultaneous equations x + y = 9 x – y = 5 2x = 14 x = 7 x + y = y = 9 y = 9 – 7 y = 2 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 ) = = 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 = 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 = 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 = 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