Question

Two of the solutions for the equation 2x + 3y = 12 are (9, { }) and ({ }, 4). What are the missing values in the solution?

A) (9, 4)
B) (3, 4)
C) (9, 2)
D) (3, 2)

Answer 1

To find the missing values for the equation 2x + 3y = 12, we substitute the known value of one variable and solve for the other. The solution for (9, { }) is (9, -2) and for ({ }, 4) is (0, 4), which are not listed in the provided answer options.

Step-by-step explanation:

To find the missing values in the solutions for the equation 2x + 3y = 12, we need to substitute the known values of x and y into the equation and solve for the unknowns.

For the solution (9, { }), we substitute x with 9:

2(9) + 3y = 12
18 + 3y = 12
3y = 12 - 18
3y = -6
y = -2

So, the missing value for y when x is 9 is -2.

For the solution ({ }, 4), we substitute y with 4:

2x + 3(4) = 12
2x + 12 = 12
2x = 12 - 12
2x = 0
x = 0

Therefore, the missing value for x when y is 4 is 0.

The solutions are (9, -2) and (0, 4), so the correct answer is not listed in the provided options A) (9, 4) B) (3, 4) C) (9, 2) D) (3, 2).