SOLUTION: solve by using the best method for each system. 3x-3y=18 and x+y=3

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Question 27654: solve by using the best method for each system.
3x-3y=18 and
x+y=3
Answer by askmemath(368) About Me  (Show Source):
You can put this solution on YOUR website!
3x-3y=18
x+y=3
Multiplying the 2nd equation with 3
3x+3y = 9
Now, adding both
6x = 27
X+=+27%2F6
X = 4.5
Putting this value back into any equation we get Y = -1.5
Solved by pluggable solver: Linear System solver (using determinant)
Solve:
+system%28+%0D%0A++++3%5Cx+%2B+-3%5Cy+=+18%2C%0D%0A++++1%5Cx+%2B+1%5Cy+=+3+%29%0D%0A++

Any system of equations:
+system%28+%0D%0A++++a%5B11%5D%2Ax+%2B+a%5B12%5D%2Ay+=+b%5B1%5D%2C%0D%0A++++a%5B21%5D%2Ax+%2B+a%5B22%5D%2Ay+=+b%5B2%5D%29%0D%0A++

has solution
+system%28+%0D%0A++++x+=+%28b%5B1%5D%2Aa%5B22%5D+-+b%5B2%5D%2Aa%5B12%5D%29%2F%28a%5B11%5D%2Aa%5B22%5D-a%5B21%5D%2Aa%5B12%5D%29%2C%0D%0A++++y+=+%28a%5B11%5D%2Ab%5B2%5D+-+a%5B21%5D%2Ab%5B1%5D%29%2F%28a%5B11%5D%2Aa%5B22%5D-a%5B21%5D%2Aa%5B12%5D%29%0D%0A++++%29%0D%0A++
or

+system%28+%0D%0A++++++x+=+%2818%2A1+-+3%2A-3%29%2F%283%2A1-1%2A-3%29+=+4.5%2C%0D%0A++++++y+=+%283%2A3+-+1%2A18%29%2F%283%2A1-1%2A-3%29+=+-1.5%0D%0A++++%29%0D%0A++

(x=4.5, y=-1.5}


Solved by pluggable solver: SOLVE linear system by SUBSTITUTION
Solve:
+system%28+%0D%0A++++3%5Cx+%2B+-3%5Cy+=+18%2C%0D%0A++++1%5Cx+%2B+1%5Cy+=+3+%29%0D%0A++We'll use substitution. After moving -3*y to the right, we get:
3%2Ax+=+18+-+-3%2Ay, or x+=+18%2F3+-+-3%2Ay%2F3. Substitute that
into another equation:
1%2A%2818%2F3+-+-3%2Ay%2F3%29+%2B+1%5Cy+=+3 and simplify: Error: 'Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. '. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115. Can't call method "invoke_solver" on an undefined value at /home/ichudov/project_locations/algebra.com/templates/Algebra/Solver/PerlSolver.pm line 115.
error_location: 101