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Determine whether each system of linear equations has (a) one and only one solution, (b) infinitely many solutions, or
(c) no solution. Find the solutions whenever they exist.
4. 3x-4y=7
There should be another equation in the question. Please check and let me know.
6. 3/2x-2y=4 x+1/3y=2
Multiply the second equation by 3/2 and subtract it from the first
(3/2)x - 2y - (3/2)x - (1/2)y = 4 - 3
(-5/2)y = 1
y = -2/5
From the second equation, x = 2 - (1/3)y = 2 - (1/3)(-2/5) = 32/15
Solution: (x, y) = (32/15, -2/5) - Only one solution
Solve the system of linear equations using the Gauss-Jordan elimination Method.
36. 3x+y=1 -7-2y= -1
Solution: (x, y) = (1, -4) - Only one solution
38. 5x+3y= 9 -2x+y= -8
Solution: (x, y) = (-3, 2) - Only one solution
44. 2x+4y-6z= 38 x+2y+3z= 7 3x-4y+4z= -19
Solution: (x, y, z) = (-3, -5, 2) - Only one solution.
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