x = Maggie's age
y = The brother's age
x + y = 42
y = 3x - 6
Using the substitution property, we can replace y in the first equation with the 3x - 6 in the second equation like so:
x + (3x - 6) = 42
Then solve this equation for x like so:
x + (3x - 6) = 42
x + 3x = 48 (Add 6 to both sides)
4x = 48 (Simplify)
x = 12 (Divide both sides by 4)
This shows that Maggie's is 12 years old. In order to prove this, you must check your work. In order to do this, first plug your answer back into the original equation like so:
x + y = 42
12 + y = 42. (Plug in answer)
y = 30 (Subtract both sides by 12)
This shows that Maggie's brother is 30 years old. The final step to proving this is to plug both of your answers into the second equation to make sure that your answers are within the constraints set by the problem. Do this like so:
y = 3x - 6
30 = 3(12) - 6 (Plug in answers)
30 = 36 - 6 (Simplify)
30 = 30 (Simplify)
Because the equation is balanced, your answers are correct. So, to answer your question, Maggie is 12 years old.
