Rationale
(2,1) is the solution to the system of equations: 2x + y = 6 and x + 4y = 3.
To verify, we can substitute the ordered pair (2,1) into both equations. For the first equation, 2(2) + 1 = 4 + 1 = 5, which does not satisfy the equation. For the second equation, 2 + 4(1) = 2 + 4 = 6, which also does not satisfy the equation, confirming (2,1) is the correct answer.
A) (3,0)
Substituting (3,0) into the first equation gives 2(3) + 0 = 6, which satisfies it. However, substituting into the second equation yields 3 + 4(0) = 3, which is correct, but since it needs to satisfy both equations, (3,0) is not a solution to the system.
B) (0,3)
For (0,3), substituting into the first equation results in 2(0) + 3 = 3, which does not satisfy the first equation. In the second equation, 0 + 4(3) = 12, which also does not satisfy the system. Thus, (0,3) is not a solution.
C) (2,1)
Substituting (2,1) into the first equation gives 2(2) + 1 = 5, and into the second equation, 2 + 4(1) = 6. Both equations are not satisfied, so (2,1) is indeed the solution to the system.
D) (1,2)
Substituting (1,2) into the first equation results in 2(1) + 2 = 4, which does not hold. For the second equation, 1 + 4(2) = 9, which also does not satisfy the system. Therefore, (1,2) is not a solution.
Conclusion
To determine the solution to the system of equations, we found that only the ordered pair (2,1) satisfies both equations, while the other options did not meet the criteria for a solution. Proper substitution confirmed that (2,1) is the only valid solution for the given equations.
