Answer:
x = 6
Explanation:
The question asks us to solve for one of the variables in the linear system, also known as a system of equations. There are multiple ways to solve for the variables, but we will be using the substitution method. To do this, we first need to set the second equation equal to y:
3x + y = 9 ⇒ y = 9 - 3x
Now, we will substitute this value of y into the first equation:
4x + 2(9 - 3x) = 6
Notice that this leaves us with only one variable in the equation, which makes it solvable.
4x + 2(9) - 2(3x) = 6
4x + 18 - 6x = 6 ⇒ -2x + 18 = 6
Subtract 18 from both sides
-2x + 18 - 18 = 6 - 18 ⇒ -2x = -12
Finally, divide both sides by 2
x = 6
Plugging this x value back into either equation will give you the value of y. However, the question only asks for one of the variables, therefore x = 6 is a valid answer.