Orange Coast College MATH A285: Chapter 202

,Let A , B ,C
Alg . exp :




x +
2
Def : The statement that CA .
E's are equal is an equation.
A = B



equationa
+1 2 S
ex : X = Not same

But same and

= ) We
say 2 equation are equivalent if

they have the same soln , Set.




Rules :




.
1
A = B is equiv to C+ A = c + B

.
2
if c + 0, A = B equiv to c A .
= e .
B X= 1213
N2 - + 4 = X X X
.
= 1 .
X

* 03
2 = X - 4 x2 = x91 ,



(FF2)" = (x-4)2 violation

*2 xx
2 =
(x 4)jx2 -




C
-




= (x -
4)(x - 4)

, CHAP 2

1
eXi
-
-
x +
y= 4 (3 ,




x 2
y
-
=



2x = 6

4
equivx + y = 4
·
y + y =
x +
y = 4
y= /
4 + (x +
y) =
C + 4x -

y=
2(x = 6 )
= X = 3
↓
(3 , 1
(x + y) + (x + y) = 6

2x = 6




:
2x = 7
ex y
-




-
14
-
ax + by = S

2 X +
dy = t

3X


For this system
+
we can have &
ax" + bx + ex + d = 0
.
1
one valuable soln (x , y) 2X : 3x3 -
2x =
x + 1
-
3
2 No soln's 3X + 1 = 2x2 + x
.
>
-




3 .
-many sol's · Sx 2y + -
z = 4
>
- graph S-D plan



·
an xi + a , 242 + 91sx = S/

+
12242 +
923 Xs "S sol sol
a21x1 .
- one , no
, D-many sols

as , X + 932 , x2 + 933 XS . =
Ss


· general myn linear system
a llX1 +
912x2 +... + air Xn = b,
...


= b2
a2(x1 + a22x( +... + aznxn



9m , X1 + am2X2 +... + amn . Xn = Im