3.1 Solving equations by Graphing 3.1 Solving equations by
Graphing
System of equations
Consistent vs. Inconsistent
Independent vs. Dependent
System of Equations
Two or more equations with the same variables.
To solve a system of equations, you must find
where the graph of the equations intersect.
Consistent vs. Inconsistent
Consistent – one or more solution
(points where the graph intersect)
Inconsistent – No solution (no intersects)
Inconsistent have the same slope.
Consistent
Inconsistent
Independent vs. Dependent
Independent – One solution (Consistent)
Dependent – Many solutions
( the same equation)
Dependent
y = 3x + 5
-6x + 2y = 10
The same line.
So all the order pairs
are the same.
In a Consistent System there can only
be one
The answer (order pair) is correct in both
equation.
3x – 7y = - 6;
-7y = -3x – 6;
X + 2y = 11;
2y = - x + 11;
3
6
y  x
7
7
1
11
y
x
2
2
Then we graph
y
3
6
x
7
7
and
y
1
11
x
2
2
Then we graph
y
3
6
x
7
7
5,3
and
y
1
11
x
2
2
There must be a better way
The rest of the chapter show a better way.
So on to Section 3.2