what is the solution of this system of linear equations?\n3y = \\frac{3}{2}x + 6\n\\frac{1}{2}y…

what is the solution of this system of linear equations?\n3y = \\frac{3}{2}x + 6\n\\frac{1}{2}y - \\frac{1}{4}x = 3\n(3, 6)\n(2, 1)\nno solution\ninfinite number of solutions

what is the solution of this system of linear equations?\n3y = \\frac{3}{2}x + 6\n\\frac{1}{2}y - \\frac{1}{4}x = 3\n(3, 6)\n(2, 1)\nno solution\ninfinite number of solutions

Answer

Explanation:

Step1: Simplify the first equation

Divide both sides of $3y=\frac{3}{2}x + 6$ by 3, we get $y=\frac{1}{2}x+2$.

Step2: Simplify the second equation

Multiply both sides of $\frac{1}{2}y-\frac{1}{4}x = 3$ by 4 to clear the fractions. We have $2y - x=12$, which can be rewritten as $y=\frac{1}{2}x + 6$.

Step3: Analyze the slopes and y - intercepts

The first equation $y=\frac{1}{2}x+2$ has a slope $m_1=\frac{1}{2}$ and y - intercept $b_1 = 2$. The second equation $y=\frac{1}{2}x + 6$ has a slope $m_2=\frac{1}{2}$ and y - intercept $b_2=6$. Since the slopes are equal ($m_1 = m_2$) and the y - intercepts are different ($b_1\neq b_2$), the two lines are parallel.

Answer:

no solution