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Sagot :
4r - 4s + 4t = - 4 (Equation 1)
4r + s - 2t = 5 (Equation 2)
-3r - 3s -4t =-16 (Equation 3)
Multiplying equation 2 by 2 and adding to equation 1, we have:
8r + 2s - 4t = 10
+ 4r -4s + 4t = -4
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12r -2s = 6 Equation(1a)
Multiplying equation 2 by -2 and adding to equation 3, we have:
-8r - 2s + 4t = -10
-3r - 3s -4t =-16
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-11r - 5s = -26 Equation (2a)
Then we solve the new system of equations (2x2)
12r -2s =6 Equation (1a)
-11r - 5s = -26 Equation (2a)
Multiplying the equation (1a) by -5 and the equation (2a) by 2, we have:
-60r + 10s = -30 Equation (1a)
-22r - 10s = -52 Equation (2a)
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-82r=-82 (Adding equation(1a) and equation(2a))
r= -82/(-82) (Dividing by -82 on both sides of the equation)
r=1
Replacing r=1 in the equation (1a)
12*(1) -2s =6
12 - 2s = 6 (Multiplying)
-2s= 6 - 12 (Subtracting 12 from both sides of the equation)
s=-6/ (-2) (Dividing by -2 on both sides of the equation)
s=3 (Dividing)
Replacing r=1, s=3 in the equation (1) , we have:
4*(1) - 4*(3) + 4t = - 4
4 - 12 + 4t = -4 (Multiplying)
- 8 + 4t = -4 (Subtracting)
4t = -4 + 8 (Adding 8 to both sides of the equation)
t = 4/4 (Dividing by 4 on both sides of the equation)
t= 1
The answer is:
r=1, s=3 and t=1.
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