Final answer:
The error in solving for one of the variables in the linear system 4x+2y=6 and 3x+y=9 is not indicated. It is necessary to use the substitution method to find the solution: x = 6, y = -9.
Step-by-step explanation:
When solving the linear system 4x+2y=6 and 3x+y=9, we can use the method of substitution or elimination to find the solution. Let's use the substitution method:
From the second equation, solve for y in terms of x: y = 9 - 3x
Substitute this expression for y into the first equation: 4x + 2(9 - 3x) = 6
Simplify and solve for x: 4x + 18 - 6x = 6, -2x = -12, x = 6
Substitute the value of x back into either of the original equations to find y: y = 9 - 3(6), y = -9
Therefore, the solution to the linear system is x = 6, y = -9.