Question

Solve the system of equations (2x - 5y = -6) and (4x - 3y = -12) using the substitution method.

a) None
b) (x = 2, y = -2)
c) (x = -2, y = 2)
d) (x = 1, y = -1)

Answer 1

By using the substitution method, the system of equations (2x - 5y = -6) and (4x - 3y = -12) is solved to find (x = 3/7, y = 12/7). Since this solution does not match any of the provided multiple-choice answers, the correct option is (a) None.

Step-by-step explanation:

To solve the system of equations (2x - 5y = -6) and (4x - 3y = -12) using the substitution method, follow these steps:

1. Solve one of the equations for one variable. For example, from the first equation 2x - 5y = -6, solve for x: x = (5y - 6)/2.
2. Substitute this expression for x into the second equation. So 4x - 3y = -12 becomes 4((5y - 6)/2) - 3y = -12.
3. Simplify and solve for y: (10y - 24) - 3y = -12, which simplifies to 7y = 12. Dividing both sides by 7 gives us y = 12/7.
4. Substitute the value of y back into the expression for x to find x: x = (5(12/7) - 6)/2.
5. Solve to find x = 3/7.
6. The solution to the system is (x = 3/7, y = 12/7), which does not match any of the given options a) None b) (x = 2, y = -2) c) (x = -2, y = 2) d) (x = 1, y = -1).

Hence, the correct choice is (a) None, as the calculated solution does not match any of the provided options.