how do i solve these quadratics? c=10000
9a+3b+c=7975
36a+6b+c=6400
im unsure of how to solve as a and b are unknowns...
Step #1 is to replace c with 10000 in both equations to get
9a + 3b = -2025 ---> 3a + b = -675
36a + 6b = -3600 --> 6a + b = -600
subtract the two equations:
3a = 75
a = 25
plug that into 3a + b = -675
75 + b = -675
b = -750
check:
9(25) + 3(-750) + 10000 = 7975 check!
36(25) + 6(-750) + 10000=6400, check!
my answers are correct
btw, these were not quadratics
I find it strange that a person taking Calculus would not know how to solve two linear equations with two unknowns.
To solve these quadratics, you'll need to use the method of substitution or elimination. First, let's rearrange the equations to isolate c:
Equation 1: 9a + 3b + c = 7975 (Equation A)
Equation 2: 36a + 6b + c = 6400 (Equation B)
To eliminate the variable c, we subtract Equation A from Equation B:
(Equation B) - (Equation A):
36a + 6b + c - (9a + 3b + c) = 6400 - 7975
36a - 9a + 6b - 3b = -1575
27a + 3b = -1575 (Equation C)
Now we have two equations with two unknowns, a and b. By solving these equations simultaneously, you can find the values of a and b.
1. METHOD OF SUBSTITUTION:
Let's solve Equation C for a in terms of b:
27a = -3b - 1575
a = (-3b - 1575) / 27
Now substitute this expression for a in either Equation A or B, let's choose Equation A:
9((-3b - 1575) / 27) + 3b + c = 7975
((-3b - 1575) / 3) + 3b + c = 7975
-3b - 1575 + 9b + 3c = 23925
6b + 3c = 25500 (Equation D)
Now we have two equations with two unknowns, b and c.
2. METHOD OF ELIMINATION:
To eliminate the variable a, multiply Equation C by 3:
3(27a + 3b) = 3(-1575)
81a + 9b = -4725 (Equation E)
Now subtract Equation E from Equation D:
(6b + 3c) - (81a + 9b) = 25500 - (-4725)
-75a - 3b + 3c = 30225
Now we have two equations with two unknowns, a and b.
You can now solve the resulting system of equations using substitution, elimination, or any other method you prefer. Once you find the values for a and b, you can substitute them back into either Equation A or B to solve for c.
Hope this explanation helps you solve the quadratics!