Transcript Simultaneous Equations

Simultaneous Equations
What are
simultaneou
s equations
27 March, 2016
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