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Algebra, Functions, Graphs, and Vectors 43

(x ,y ) ( 3,4)
1
1
(x ,y ) (0,1)
2
2
Example B. Consider the following twm equations:

2
y 2x 4x 5
y 2x 5

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

2
2x 5 2x 4x 5

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

2
2x 5 2x 4x 5
2
2x 2x 4x
2
0 2x 6x
2
2x 6x 0 0
Using the quadratic formula, let a 2, b 6, and c 0:

2
x ( 6 (6 4 2 0) 1/2 )/(2 2)
x ( 6 (36 0) 1/2 )/ 4

x ( 6 6)/ 4

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

y 2 3 5 and y 2 0 5
1
2
y 11 and y 5
2
1
The solutionð are therefore: