Question

convert the equations in the system below into slope - intercept form and then classify the system.
6x - 7y = 2
24x - 28y = 11
in slope - intercept form, the first equation is y =
in slope - intercept form, the second equation is y =
the system is...
consistent - dependent
consistent and independent
inconsistent

Explanation:

Step1: Rearrange first equation for y

Starting with $6x - 7y=2$, subtract $6x$ from both sides: $- 7y=-6x + 2$. Then divide by $-7$: $y=\frac{6}{7}x-\frac{2}{7}$.

Step2: Rearrange second equation for y

Starting with $24x - 28y = 11$, subtract $24x$ from both sides: $-28y=-24x + 11$. Then divide by $-28$: $y=\frac{6}{7}x-\frac{11}{28}$.

Step3: Analyze the system

The slopes of the two lines are the same ($m = \frac{6}{7}$) but the y - intercepts ($b_1=-\frac{2}{7}$ and $b_2 = -\frac{11}{28}$) are different. So the lines are parallel and the system has no solution.

Answer:

In slope - intercept form, the first equation is $y=\frac{6}{7}x-\frac{2}{7}$
In slope - intercept form, the second equation is $y=\frac{6}{7}x-\frac{11}{28}$
The system is Inconsistent