Lesson Intro to Systems
When you solve one variable equations
When you solve one variable equations
2x - 4 = 6
When you solve one variable equations
2x - 4 = 6
+4
+4
Add 4 to both sides
When you solve one variable equations
2x - 4 = 6
2x = 10
+4
+4
Fill in the correct value
When you solve one variable equations
2x - 4 = 6
2x = 10
+4
2
+4
2
When you solve one variable equations
2x - 4 = 6
2x = 10
+4
2
x = 5
+4
2
When you solve one variable equations
2x - 4 = 6
2x = 10
+4
2
x = 5
+4
2
You are solving for the number that can go in for x
When you solve one variable equations
2x - 4 = 6
2x = 10
+4
2
x = 5
+4
2
You are solving for the number that can go in for x
When you solve one variable equations
2x - 4 = 6
2x - 4 = 6
2x = 10
+4
2
x = 5
+4
2
You are solving for the number that can go in for x
When you solve one variable equations
2x - 4 = 6
2x - 4 = 6
2x = 10
+4
2
x = 5
x = 5
+4
2
You are solving for the number that can go in for x
When you solve one variable equations
2x - 4 = 6
2x - 4 = 6
2x = 10
+4
2
x = 5
x = 5
+4
2
2( 5 ) -4 = 6
You are solving for the number that can go in for x
When you solve one variable equations
2x - 4 = 6
2x - 4 = 6
2x = 10
+4
2
x = 5
x = 5
+4
2
2( 5 ) -4 = 6
10 - 4 = 6
For a two variable equations
For a two variable equations
x + y = 5
There are many sets of possible solutions
For a two variable equations
x + y = 5
x = 1
There are many sets of possible solutions
y = 4
For a two variable equations
because 1 + 4 = 5
x + y = 5
x =2
x = 1
Fill in the correct value
There are many sets of possible solutions

y = 3

y = 4
For a two variable equations
because 2 + 3 = 5
because 1 + 4 = 5
x + y = 5
x =2
x = 100
x = 1
There are many sets of possible solutions

y = 3

y = 4
y = -95
For a two variable equations
because 2 + 3 = 5
because 1 + 4 = 5
because 100 - 95 = 5
x + y = 5
Fill in the correct value
x =2
x = 100
x = 1
In fact, the number of solutions are infinite
There are many sets of possible solutions

y = 3

y = 4
y = -95
For a two variable equations
because 2 + 3 = 5
because 1 + 4 = 5
because 100 - 95 = 5
x + y = 5
But if I have two equations
But if I have two equations
x + y = 5
x - y = -3
But if I have two equations
each with two variables
x + y = 5
x - y = -3
I can solve for the x and y values that work for BOTH
But if I have two equations
each with two variables
x + y = 5
x - y = -3
I can solve for the x and y values that work for BOTH
Solutions
Possible
But if I have two equations
each with two variables
x + y = 5
x - y = -3
I can solve for the x and y values that work for BOTH
x = 0  y = 5
Solutions
Possible
But if I have two equations
each with two variables
x + y = 5
x - y = -3
x = 1  y = 4
I can solve for the x and y values that work for BOTH
x = 0  y = 5
Solutions
Fill in the correct value
Possible
But if I have two equations
each with two variables
x + y = 5
x - y = -3
x = 2  y = 3
x = 1  y = 4
I can solve for the x and y values that work for BOTH
x = 0  y = 5
Solutions
Possible
Fill in the correct value
But if I have two equations
each with two variables
x + y = 5
x - y = -3
x = 2  y = 3
x = 1  y = 4
I can solve for the x and y values that work for BOTH
x = 0  y = 5
Solutions
Possible
But if I have two equations
each with two variables
x + y = 5
x - y = -3
Solutions
Possible
x = 2  y = 3
x = 1  y = 4
I can solve for the x and y values that work for BOTH
x = 0  y = 5
Solutions
Possible
But if I have two equations
each with two variables
x + y = 5
x - y = -3
x = 0  y = 3
Solutions
Possible
x = 2  y = 3
x = 1  y = 4
I can solve for the x and y values that work for BOTH
x = 0  y = 5
Solutions
Possible
But if I have two equations
each with two variables
x + y = 5
x - y = -3
x = 0  y = 3
x = 1  y = 4
Solutions
Possible
x = 2  y = 3
x = 1  y = 4
I can solve for the x and y values that work for BOTH
x = 0  y = 5
Solutions
Possible
But if I have two equations
each with two variables
x + y = 5
x - y = -3
x = 2  y = 5
x = 0  y = 3
x = 1  y = 4
Solutions
Possible
x = 2  y = 3
x = 1  y = 4
I can solve for the x and y values that work for BOTH
x = 0  y = 5
Solutions
Possible
But if I have two equations
The set that matches
each with two variables
x + y = 5
x - y = -3
x = 2  y = 5
x = 0  y = 3
x = 1  y = 4
Solutions
Possible
x = 2  y = 3
x = 1  y = 4
I can solve for the x and y values that work for BOTH
x = 0  y = 5
Solutions
Possible
But if I have two equations
The set that matches
each with two variables
is the answer
x + y = 5
x - y = -3
x = 2  y = 5
x = 0  y = 3
x = 1  y = 4
Solutions
Possible
x = 2  y = 3
x = 1  y = 4
I can solve for the x and y values that work for BOTH
x = 0  y = 5
Solutions
Possible
But if I have two equations
The set that matches
each with two variables
is the answer
x + y = 5
x - y = -3
x = 2  y = 5
x = 0  y = 3
x = 1  y = 4
Solutions
Possible
x = 2  y = 3
x = 1  y = 4
I can solve for the x and y values that work for BOTH
x = 0  y = 5
Solutions
Possible
But if I have two equations
The set that matches
each with two variables
is the answer
x + y = 5
x - y = -3
x = 2  y = 5
x = 0  y = 3
x = 1  y = 4
Solutions
Possible
x = 2  y = 3
x = 1  y = 4
I can solve for the x and y values that work for BOTH
x = 0  y = 5
Solutions
Possible
x = 1 and y = 4 is the answer
But if I have two equations
The set that matches
each with two variables
is the answer
x + y = 5
x - y = -3
x = 2  y = 5
x = 0  y = 3
x = 1  y = 4
Solutions
Possible
x = 1 and y = 4 is the answer
x + y = 5
x - y = -3
That means that
x = 1 and y = 4 is the answer
x + y = 5
x - y = -3
That means that
x = 1 and y = 4 is the answer

if I put 1 in for x

x + y = 5
x - y = -3
That means that
x = 1 and y = 4 is the answer

if I put 1 in for x

and 4 in for y
x + y = 5
x - y = -3
That means that
x = 1 and y = 4 is the answer

if I put 1 in for x

and 4 in for y
both equations will be correct
x + y = 5
x - y = -3
That means that
x = 1 and y = 4 is the answer

if I put 1 in for x

and 4 in for y
both equations will be correct
x + y = 5
x - y = -3
1 + 4 = 5
That means that
x = 1 and y = 4 is the answer

if I put 1 in for x

and 4 in for y
both equations will be correct
x + y = 5
x - y = -3
1 + 4 = 5
1 - 4 = -3
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