Simultaneous Equations What are simultaneous equations 322021 Let

Simultaneous Equations What are simultaneous equations 3/2/2021 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=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 2. y 3. 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 3. (+ y) and (– y) have different signs so ADD

x+y=9 x–y=5 2 x = 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 3. x + x = 2 x and (+ y ) + (- y ) = 0 4. and 9 + 5 = 14

x+y=9 x–y=5 2 x = 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 4. 2 x = 14 5. x = 14 ÷ 2 6. x = 7

x+y=9 x–y=5 2 x = 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 5. 7 + y = 9 6. y=9– 7 7. y=2

Here is another pair of simultaneous equations 2 x + y = 11 x–y=4 To solve, follow the steps

2 x + y = 11 x–y= 4 3 x = 15 1. Make sure that the middles are the same 2. If the signs are different ADD 2 x + x = 3 x (+ y) + (– y ) = 0 11 + 4 = 15

2 x + y = 11 x–y= 4 3 x = 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 3 x = 15 ÷ 3 x=5

2 x + y = 11 x–y=4 3 x = 15 x=5 2 x + 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

2 x + y = 11 x–y=4 3 x = 15 x=5 2 x + y = 11 10 + 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 2 x + y = 14 x+y=4 The same

2 x + y = 14 x+y =9 x =5 2 x + y = 14 10 + 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 3. If the signs are Different ADD 4. 3. Find the value of x 5. 4. Use this to find the value of y