which statements about the system are true? select two options.\ny = \\frac{1}{3}x - 4\n3y - x = -7\n□ the…

which statements about the system are true? select two options.\ny = \\frac{1}{3}x - 4\n3y - x = -7\n□ the system has one solution.\n□ the system consists of parallel lines.\n□ both lines have the same slope.\n□ both lines have the same y - intercept.\n□ the equations represent the same line.

which statements about the system are true? select two options.\ny = \\frac{1}{3}x - 4\n3y - x = -7\n□ the system has one solution.\n□ the system consists of parallel lines.\n□ both lines have the same slope.\n□ both lines have the same y - intercept.\n□ the equations represent the same line.

Answer

Explanation:

Step1: Rewrite the second - equation in slope - intercept form

Given $3y - x=-7$, solve for $y$. Add $x$ to both sides: $3y=x - 7$. Then divide by 3: $y=\frac{1}{3}x-\frac{7}{3}$.

Step2: Analyze the slopes and y - intercepts

The first equation is $y = \frac{1}{3}x-4$. The second equation is $y=\frac{1}{3}x-\frac{7}{3}$. The slope of the first line $m_1=\frac{1}{3}$ and the y - intercept $b_1=-4$. The slope of the second line $m_2=\frac{1}{3}$ and the y - intercept $b_2 =-\frac{7}{3}$. Since the slopes are equal ($m_1 = m_2=\frac{1}{3}$) and the y - intercepts are different ($b_1\neq b_2$), the lines are parallel. Parallel lines have no solution.

Answer:

The system consists of parallel lines. Both lines have the same slope.