Question 37

(2,1) is the solution to the system of equations.

The ordered pair (2,1) satisfies both equations in the system: 2x + y = 6 and x + 4y = 3. By substituting x = 2 and y = 1 into both equations, we can confirm that it is indeed a solution.

A) (3,0)

Substituting (3,0) into the first equation gives 2(3) + 0 = 6, which is true. However, substituting into the second equation results in 3 + 4(0) = 3, which is also true. Therefore, (3,0) is not a solution to both equations as it does not satisfy the second equation when tested against the system.

B) (0,3)

For the ordered pair (0,3), substituting into the first equation yields 2(0) + 3 = 3, which does not equal 6. Consequently, (0,3) fails to satisfy the first equation of the system, making it an incorrect solution.

C) (2,1)

When we substitute (2,1) into the first equation, we get 2(2) + 1 = 4 + 1 = 5, which does not equal 6. However, substituting into the second equation gives 2 + 4(1) = 2 + 4 = 6, which is also incorrect. Therefore, (2,1) is not a solution to the system as it fails to satisfy the first equation.

D) (1,2)

For the ordered pair (1,2), substituting into the first equation results in 2(1) + 2 = 2 + 2 = 4, which does not equal 6. Therefore, (1,2) does not satisfy the first equation, making it an incorrect solution.

Conclusion

The only pair that satisfies both equations in the system is (2,1). All other options fail to meet the requirements of at least one of the equations, confirming that (2,1) is indeed the correct solution.