Simultaneous Equations 20 May, 2019 Let me explain. If you have an equation like: x + y = 5, there are lots of answers. What are simultaneous equations

x + y = 5 x = 4 y = 1 4 + 1 = 5 x = 3 y = 2 3 + 2 = 5 x = 2 y = 3 Here are some of these answers 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 x – y = 1 Like this

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

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

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

Here is a method for solving simultaneous equations x + y = 9 x – y = 5 2x = 14 x = 7 Make sure that the middles are the same If the signs are different ADD 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 7 + y = 9 y = 9 – 7 y = 2 Here is a method for solving simultaneous equations Make sure that the middles are the same If the signs are different ADD Find the value of x 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 2x + x = 3x (+ y) + (– y ) = 0 Make sure that the middles are the same 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 Make sure that the middles are the same If the signs are different ADD Find the value of x 3x = 15 x = 15 ÷ 3 x = 5

2x + y = 11 x – y = 4 3x = 15 x = 5 10 + y = 11 Make sure that the middles are the same If the signs are different ADD Find the value of x Use this to find the value of y

2x + y = 11 x – y = 4 3x = 15 x = 5 10 + y = 11 y = 11 – 10 y = 1 Make sure that the middles are the same If the signs are different ADD Find the value of x 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 10 + y = 14 y = 14 – 10 y = 4 Make sure that the middles are the same If the signs are the same SUBTRACT Find the value of x Use this to find the value of y

Make sure that the middles are the same 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