Elimination method:
a. 3x+4y= -7
b. 2x+3y= -6

well from your first one you find that

3x = -7-4y

so

x = -7/3 - 4y/3

now you can substitute this in for x in your second equation

2(-7/3 - 4y/3) + 3y = -6

you can now solve this for y to get a value of y

then you can use your original equations and this value of y to find the value for x

let me know if you need further help

Capuchin she specifically said elimination method. What you did was the substitution method.