Question

what is the solution of this system of linear equations?
$3y = \frac{3}{2}x + 6$
$\frac{1}{2}y - \frac{1}{4}x = 3$
○ (3, 6)
○ (2, 1)
○ no solution
○ infinite number of solutions

Explanation:

Step1: Simplify first equation

Divide all terms by 3:
$$y = \frac{1}{2}x + 2$$

Step2: Simplify second equation

Multiply all terms by 4 to eliminate fractions:
$$2y - x = 12$$
Rearrange to solve for $y$:
$$2y = x + 12$$
$$y = \frac{1}{2}x + 6$$

Step3: Compare the two lines

The two equations are $y = \frac{1}{2}x + 2$ and $y = \frac{1}{2}x + 6$. They have the same slope ($\frac{1}{2}$) but different y-intercepts (2 vs. 6), meaning they are parallel and never intersect.

Answer:

no solution