Question

Solve the system of equations -3r +3s+t = 13, -4r-5s-5t=30, and -5r+6s+5t=15

Answer 1

To solve the system of equations -3r +3s+t = 13, -4r-5s-5t=30, and -5r+6s+5t=15, you can eliminate variables and solve for the remaining variables. By eliminating t and s, you can find the values of r, s, and t. The solution is r = 5, s ≈ -34.83, t = 132.5.

Step-by-step explanation:

To solve the system of equations -3r +3s+t = 13, -4r-5s-5t=30, and -5r+6s+5t=15:

1. Choose any two equations and eliminate one variable. Let's eliminate t. We can multiply the first equation by 5, the second equation by 3, and the third equation by 2 to make the coefficients of t the same in all three equations. This gives us:
2. -15r +15s+5t = 65
3. -12r-15s-15t=90
4. -10r+12s+10t=30
5. Add these equations together to eliminate t. This gives us:
6. -37r +12s+ 0 = 185
7. Now, choose any two pairs of equations and eliminate another variable. Let's eliminate s. Multiply the first equation by 15, the second equation by 37, and the third equation by 5 to make the coefficients of s the same in all three equations. This gives us:
8. -45r + 45s+15t = 195
9. -37r - 37s - 37t = 1110
10. -50r + 60s + 50t = 150
11. Add these equations together to eliminate s. This gives us:
12. -32r + 8t = 900
13. Now, solve for t by substituting the value of r into this equation:
14. -32(5) + 8t = 900
15. -160 + 8t = 900
16. 8t = 1060
17. t = 132.5
18. Finally, substitute the values of r and t into one of the original equations to solve for s:
19. -3(5) + 3s + 132.5 = 13
20. -15 + 3s + 132.5 = 13
21. 3s + 117.5 = 13
22. 3s = -104.5
23. s = -34.83

So, the solution to the system of equations is:

r = 5, s ≈ -34.83, t = 132.5