Example
1:
Solve the following equations
X + y = 8
,
x y – 15 = 0
the answer :
from the first equation :
y = 8 – x
Substitute the expression 8 – x for y into the second equation and solve for x
X ( 8 – x ) – 15 = 0
8 x – x2 – 15 = 0 …….. × - 1
X2 – 8
x + 15 =0
( x – 3 ) ( x – 5
) = 0
x = 3 or x = 5
y = 8 - x =8 - 3 y = 8 -x =8 - 5
y= 5 y= 3
the solution to
this equations = {(3, 5) ,( 5 , 3) }
Example 2:
Solve the following equations
X + y = 7 , x y – 12 = 0
the answer :
from the first equation : y = 7 – x
Substitute the expression 7 – x for y into the second equation and solve for
x
X ( 7 – x ) – 12= 0
…………..
…………….
the solution to
this equations = {(3, 4) ,( 4 , 3) }
Example 3
:
Solve the following equations
X + y = 10 , x y = 16
the answer :
from the first equation : y = 10 – x
Substitute the expression 10 – x for y into the second equation and solve for
x
X ( 10 – x ) – 16 = 0
10 x – x2 – 16 = 0 …….. × - 1
X2 – 10
x + 16 =0
…………..
the solution to
this equations = {(2, 8) ,( 8 , 2) }
Example 4:
Solve the following equations
X = y , x2
+ y2 = 50
the answer :
Substitute x for y into the second
equation and solve for x
X2
+ x2 = 50
2 x2 = 50
X2 =25
x = 5 or x = - 5
y =
x y = x
y= 5 y= - 5
the solution to
this equations = { (5, 5) , ( - 5 , - 5 ) }
Example 5
:
Solve the following equations
X + y = 6 , x2 – y2
= 24
the answer :
from the first equation : x = 6 – y
Substitute the expression 6 – y for x into the second equation and solve for y
( 6 – y )2 – y2 = 24
36 – 12 y + y2 – y2
= 24
- 12 y = -36 + 24
- 12 y = -12
Y = 1
X + y = 6
x + 1 = 6
x = 5
the solution to this equations = {(5, 1) }
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