Question

Which of the following solutions solves the system? 4x + 3y = 19 7x − 6y = -23

a) (-1, 3)

b) (1, 5)

c) (1, 7)

d) None of these choices are correct.

Answer 1

To solve the system of equations, we substitute each solution into the equations and check if they satisfy both equations. The solution that solves the system is (1, 5). Hence the correct answer is option B

Step-by-step explanation:

To find which of the given solutions solves the system of equations:

4x + 3y = 19

7x − 6y = -23

we need to substitute each solution into the equations and check if they satisfy both equations.

1. For solution a) (-1, 3):
   When x = -1 and y = 3, we have:
   4(-1) + 3(3) = 19 ==> -4 + 9 = 19 ==> 5 = 19 (false)
2. For solution b) (1, 5):
   When x = 1 and y = 5, we have:
   4(1) + 3(5) = 19 ==> 4 + 15 = 19 ==> 19 = 19 (true)
3. For solution c) (1, 7):
   When x = 1 and y = 7, we have:
   4(1) + 3(7) = 19 ==> 4 + 21 = 19 ==> 25 = 19 (false)
4. For solution d) None of these choices are correct:
   Since this option states none of the given choices are correct, it can be disregarded as a solution.

Therefore, the solution that solves the system of equations is b) (1, 5).