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Lesson XYT
Contributed by: Pappal
When dealing with an equation with one variable
When dealing with an equation with one variable

2x + 5 = 11

When dealing with an equation with one variable
You generally get one solution

2x + 5 = 11

x =
that can be put in for x to make the equation work
This means that the number
When dealing with an equation with one variable
You generally get one solution

2x + 5 = 11

x = 3
is the only number
that can be put in for x to make the equation work
This means that the number 3 is the only  number
When dealing with an equation with one variable
You generally get one solution

2x + 5 = 11

2(3) + 5 = 11
x = 3
+ 5 = 11
But with two variable equations
But with two variable equations
x + y = 5
There is not only one set of answers that work
But with two variable equations
x + y = 5
There is not only one set of answers that work
But with two variable equations
x = 2      y = 3
x + y = 5
There is not only one set of answers that work
But with two variable equations
x = 2      y = 3
x + y = 5
2 + 3 = 5
There is not only one set of answers that work
But a variety of answers that will work
But with two variable equations
x = 2      y = 3
x + y = 5
2 + 3 = 5
x = 1     y = 4
1 + 4 = 5
There is not only one set of answers that work
But a variety of answers that will work
But with two variable equations
x = 2      y = 3
x + y = 5
2 + 3 = 5
x = 1     y = 4
1 + 4 = 5
There is not only one set of answers that work
But a variety of answers that will work
But with two variable equations
x = 2      y = 3
x + y = 5
x = 0    y = 5
2 + 3 = 5
0 + 5 = 5
x = 1     y = 4
1 + 4 = 5
There is not only one set of answers that work
But a variety of answers that will work
But with two variable equations
x = 2      y = 3
x + y = 5
x = 0    y = 5
2 + 3 = 5
0 + 5 = 5
x = 5    y = 0
5 + 0 = 5
x = 1     y = 4
1 + 4 = 5
There is not only one set of answers that work
But a variety of answers that will work
But with two variable equations
x = 2      y = 3
x + y = 5
x = 0    y = 5
2 + 3 = 5
0 + 5 = 5
x = 5    y = 0
5 + 0 = 5
In fact, the number of sets of answers is infinite
In fact, the number of sets of answers is infinite
x + y = 5
x = -1   y = 6
-1 + 6 = 5
In fact, the number of sets of answers is infinite
x + y = 5
x = -1   y = 6
-1 + 6 = 5
In fact, the number of sets of answers is infinite
x = 6   y = -1
x + y = 5
6 + -1 = 5
x = -1   y = 6
-1 + 6 = 5
In fact, the number of sets of answers is infinite
x = 6   y = -1
x + y = 5
6 + (-1) = 5
x = 100   y = -95
100 + (-95) = 5
x = 0.5   y = 4.5
x = -1   y = 6

0.5 + 4.5 = 5

-1 + 6 = 5
In fact, the number of sets of answers is infinite
x = 6   y = -1
x + y = 5
6 + (-1) = 5
x = 100   y = -95
100 + (-95) = 5
x = 0.5   y = 4.5
x = -1   y = 6

0.5 + 4.5 = 5

-1 + 6 = 5
In fact, the number of sets of answers is infinite
x = 4.9   y = 0.1
x = 6   y = -1
4.9 + 0.1 = 5
x + y = 5
6 + (-1) = 5
x = 100   y = -95
100 + (-95) = 5
x = 0.5   y = 4.5
x = -1   y = 6

0.5 + 4.5 = 5

-1 + 6 = 5
In fact, the number of sets of answers is infinite
x = 4.9   y = 0.1
x = 6   y = -1
4.9 + 0.1 = 5
x + y = 5
6 + (-1) = 5
x = -6.1   y = 11.1
x = 100   y = -95
-6.1 + 11.1 = 5
100 + (-95) = 5
x = 0.5   y = 4.5
x = -1   y = 6

0.5 + 4.5 = 5

-1 + 6 = 5
In fact, the number of sets of answers is infinite
x = 4.9   y = 0.1
x = 6   y = -1
4.9 + 0.1 = 5
x + y = 5
6 + (-1) = 5
x = -6.1   y = 11.1
x = 100   y = -95
-6.1 + 11.1 = 5
100 + (-95) = 5
x = 0.5   y = 4.5
x = -1   y = 6

0.5 + 4.5 = 5

-1 + 6 = 5
In fact, the number of sets of answers is infinite
x = 1,000,000   y = -999,995
1,000,000 + (-999,995) = 5
x = 4.9   y = 0.1
x = 6   y = -1
4.9 + 0.1 = 5
x + y = 5
6 + (-1) = 5
x = -6.1   y = 11.1
x = 100   y = -95
-6.1 + 11.1 = 5
100 + (-95) = 5
We can make a chart of several of these sets
We can make a chart of several of these sets
x + y = 5
We can make a chart of several of these sets
x
y
x + y = 5
We can make a chart of several of these sets
x
0
y
x + y = 5
We can make a chart of several of these sets
x
0
y
x + y = 5
Put zero in for x
We can make a chart of several of these sets
x
0
y
x + y = 5
Put zero in for x
0 + y = 5
We can make a chart of several of these sets
x
0
y
x + y = 5
Put zero in for x
and solve for y
0 + y = 5
We can make a chart of several of these sets
x
0
y
x + y = 5
Put zero in for x
and solve for y
0 + y = 5
y = 5
We can make a chart of several of these sets
x
0
5
y
Put the value for y back in the chart
x + y = 5
Put zero in for x
and solve for y
0 + y = 5
y = 5
We can make a chart of several of these sets
x
0
1
5
y
x + y = 5
Then put one in for x
We can make a chart of several of these sets
x
0
1
5
y
x + y = 5
And repeat the process
Then put one in for x
of solving for y
We can make a chart of several of these sets
x
0
1
5
y
x + y = 5
And repeat the process
Then put one in for x
of solving for y
1 + y = 5
We can make a chart of several of these sets
x
0
1
5
y
x + y = 5
And repeat the process
Then put one in for x
of solving for y
-1
1 + y = 5
-1
We can make a chart of several of these sets
x
0
1
5
y
x + y = 5
And repeat the process
Then put one in for x
of solving for y
-1
1 + y = 5
y = 4
-1
We can make a chart of several of these sets
x
0
1
4
5
y
x + y = 5
And repeat the process
Then put one in for x
of solving for y
-1
1 + y = 5
y = 4
-1
x
y
This table has many names
x
y
This table has many names
X Y T
x
y
This table has many names

T Table

X Y T
x
y
This table has many names
X Y Chart

T Table

X Y T
x
y
This table has many names
X Y Chart
X Y Table

T Table

X Y T
x
y
This table has many names
Graphing Table
X Y Chart
X Y Table

T Table

X Y T
x
y
But it is just used to keep track of
all the possible sets of answers
for a two variable equation
0
x
5
y
But it is just used to keep track of
all the possible sets of answers
for a two variable equation
0 + 5 = 5
x + y = 5
0
1
x
5
4
y
But it is just used to keep track of
all the possible sets of answers
for a two variable equation
0 + 5 = 5
1 + 4 = 5
x + y = 5
0
1
2
x
5
4
3
y
But it is just used to keep track of
all the possible sets of answers
for a two variable equation
0 + 5 = 5
1 + 4 = 5
2 + 3 = 5
x + y = 5
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