SOLUTION: Find the numbers that make both equations true: B-D=7 and B.D=60 R+T=21 and 98/T=R Please help me explain how to solve this algebraically, I know what the answers are.

Question 583756: Find the numbers that make both equations true:
B-D=7 and B.D=60
R+T=21 and 98/T=R
Please help me explain how to solve this algebraically, I know what the answers are.
Found 2 solutions by dfrazzetto, lwsshak3:
Answer by dfrazzetto(283) (Show Source): You can put this solution on YOUR website!
B-D=7 and B.D=60
B = 60/D
60/D - D/1 = 7
60 - D^2 = 7D
D^2 + 7D - 60
(D + 12)(D - 5)
D = -12, 5
5,12 and -5,-12

Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
Find the numbers that make both equations true:
B-D=7 and B.D=60
R+T=21 and 98/T=R
Please help me explain how to solve this algebraically, I know what the answers are.
**
What you have here is a system of equations which can best be solved by the substitution method:
First System:
B-D=7
B=7+D
..
B*D=60
(7+D)*D=60
7D+D^2=60
D^2+7D-60=0
(D+12)(D-5)=0
D=-12
B=7+D=-5
or
D=5
B=7+D=12
Graphically, this shows you have two points of intersection: (-12,-5) and (12,5)
..
Second system:
R+T=21
R=21-T
..
98/T=R
98/T=21-T
98=21T-T^2
T^2-21T+98=0
(T-14)(T-7)=0
T=14
R=21-14=7
or
T=7
R=21-7=14
Graphically, this shows you have two points of intersection: (14,7) and (7,14)
..
Note: Perhaps you might find it easier to work with this problem by using the more familiar notation of x and y for B and D in the first system and for R and T in the second system

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