Final answer:
To solve the system of equations 3x + 2y = 6 and -3x + y = 12 using the elimination method, multiply the second equation by 2 to make the coefficients of y in both equations the same. Then, add the equations to eliminate the variable x. The ordered pair of solutions is (-2, 6).
Step-by-step explanation:
To solve the system of equations 3x + 2y = 6 and -3x + y = 12 using the elimination method, multiply the second equation by 2 to make the coefficients of y in both equations the same. Then, add the equations to eliminate the variable x.
3x + 2y = 6
-6x + 2y = 24
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-3x + y = 12
Now, solve the resulting equation -3x + y = 12 independently. Substitute the value of x in terms of y (-3x = y - 12) from this equation into any of the original equations to find the value of y. After finding y, substitute it back into any of the equations to find the value of x.
Therefore, the ordered pair of solutions is (-2, 6).