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