Question

find the solution set for the system of equations.
question
\\(\frac{1}{3}x - \frac{1}{4}y = 1\\)
\\(\frac{2}{3}x - \frac{1}{2}y = 1\\)
select a single answer
{\\(9/4, -1\\)}
\\(\emptyset\\) (inconsistent system)
{\\(-9/4, -2\\)}
{\\(-9/4, -1\\)}

Explanation:

Step1: Eliminate fractions in Eq1

Multiply Eq1 by 12:
$$4x - 3y = 12$$

Step2: Eliminate fractions in Eq2

Multiply Eq2 by 6:
$$4x - 3y = 6$$

Step3: Compare the two equations

Subtract the new Eq2 from new Eq1:
$$(4x-3y)-(4x-3y)=12-6$$
$$0=6$$

Step4: Conclude system consistency

$0=6$ is a false statement, so the system has no solutions.

Answer:

$\emptyset$ (inconsistent system)