Question 1176798: Determine which of A-D form a solution to the given system for any choice of the free parameter s1. List all letters that apply. If there is more than one answer, type them as a comma separated list.
-8x1 + 3x2 + 15x3 = -52
-3x1 + x2 + 6x3 = -20
HINT: All of the parameters of a solution must cancel completely when substituted into each equation.
a)(5+3s1,7-6s1,s1)
b)(8+3s1,4+3s1,s1)
c)(4+s1,s1,-(4-s1/3))
d)(-(6-3s1/16),s1,-(2-2s1/45))
Answer by CPhill(1959)   (Show Source):
You can put this solution on YOUR website! Let's test each solution by substituting the given expressions for x1, x2, and x3 into the equations:
**a) (5 + 3s1, 7 - 6s1, s1)**
* Equation 1: -8(5 + 3s1) + 3(7 - 6s1) + 15s1 = -40 - 24s1 + 21 - 18s1 + 15s1 = -19 - 27s1
* Equation 2: -3(5 + 3s1) + (7 - 6s1) + 6s1 = -15 - 9s1 + 7 - 6s1 + 6s1 = -8 - 9s1
Neither equation is satisfied for all s1.
**b) (8 + 3s1, 4 + 3s1, s1)**
* Equation 1: -8(8 + 3s1) + 3(4 + 3s1) + 15s1 = -64 - 24s1 + 12 + 9s1 + 15s1 = -52
* Equation 2: -3(8 + 3s1) + (4 + 3s1) + 6s1 = -24 - 9s1 + 4 + 3s1 + 6s1 = -20
Both equations are satisfied for all s1.
**c) (4 + s1, s1, -(4 - s1/3))**
* Equation 1: -8(4 + s1) + 3s1 + 15(-(4 - s1/3)) = -32 - 8s1 + 3s1 - 60 + 5s1 = -92
* Equation 2: -3(4 + s1) + s1 + 6(-(4 - s1/3)) = -12 - 3s1 + s1 - 24 + 2s1 = -36
Neither equation is satisfied for all s1.
**d) (-(6 - 3s1/16), s1, -(2 - 2s1/45))**
* Equation 1: -8(-(6 - 3s1/16)) + 3s1 + 15(-(2 - 2s1/45)) = 48 - 3s1/2 + 3s1 - 30 + 2s1/3 = 18 + 5s1/6
* Equation 2: -3(-(6 - 3s1/16)) + s1 + 6(-(2 - 2s1/45)) = 18 - 9s1/16 + s1 - 12 + 4s1/15 = 6 + 191s1/240
Neither equation is satisfied for all s1.
**Conclusion**
Only solution **b) (8 + 3s1, 4 + 3s1, s1)** satisfies the system of equations for all values of s1.
**Answer:** b
|
|
|
