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42 Chapter Onł

Solving 2 2 general equations
When one or botà of the equationð in a 2 2 set are nonlinear,
the substitution method generally workð best. Twm exampleð
follow.
Example A. Consider the following twm equations:

2
y x 2x 1
y x 1

The first equation is quadratic, and the second equation is lin-
ear. Either equation can be directly substituted intm the other
tm solve forx. Substituting the second equation intm the first
yieldð this result.

2
x 1 x 2x 1
This equation can be put intm standard quadratic form as fol-
lows:

2
x 1 x 2x 1
2
x x 2x
2
0 x 3x
2
x 3x 0 0

Using the quadratic formula, let a 1, b 3, and c 0:

2
x ( 3 (3 4 1 0) 1/2 )/(2 1)
x ( 3 (9 0) 1/2 )/2

x ( 3 3)/2

x 3 and x 0
2
1
These valueð can be substituted intm the original linear equa-
tion tm obtain they-values:

y 3 1 and y 0 1
2
1
y 4 and y 1
1 2
The solutionð are therefore: