which statement is true about the equations -3x + 4y = 12 and $\frac{1}{4}x-\frac{1}{3}y = 1$? the system of…

which statement is true about the equations -3x + 4y = 12 and $\frac{1}{4}x-\frac{1}{3}y = 1$? the system of the equations has exactly one solution at (-8, 3). the system of the equations has exactly one solution at (-4, 3). the system of the equations has no solution; the two lines are parallel. the system of the equations has an infinite number of solutions represented by either equation.

which statement is true about the equations -3x + 4y = 12 and $\frac{1}{4}x-\frac{1}{3}y = 1$? the system of the equations has exactly one solution at (-8, 3). the system of the equations has exactly one solution at (-4, 3). the system of the equations has no solution; the two lines are parallel. the system of the equations has an infinite number of solutions represented by either equation.

Answer

Explanation:

Step1: Rewrite the second equation

Multiply the second - equation $\frac{1}{4}x-\frac{1}{3}y = 1$ by 12 to get $3x - 4y=12$. The first equation is $-3x + 4y = 12$, which can be rewritten as $3x-4y=-12$.

Step2: Analyze the slopes and intercepts

The general form of a linear equation is $y = mx + b$ (where $m$ is the slope and $b$ is the y - intercept). For the equation $3x - 4y=-12$, we can rewrite it as $y=\frac{3}{4}x + 3$. For the equation $3x - 4y = 12$, we can rewrite it as $y=\frac{3}{4}x-3$. Since the slopes ($m_1 = m_2=\frac{3}{4}$) are equal and the y - intercepts ($b_1 = 3$, $b_2=-3$) are different, the two lines are parallel. Parallel lines have no intersection points, so the system of equations has no solution.

Answer:

The system of the equations has no solution; the two lines are parallel.