Question

convert the equations in the system below into slope - intercept form and then classify the system.
4x + 11y = - 3

• 8x - 22y = 6

in slope - intercept form, the first equation is y=
in slope - intercept form, the second equation is y=
the system is...
○ consistent - dependent
○ inconsistent
○ consistent and independent
question help: written example

Explanation:

Step1: Rearrange first equation for y

Starting with $4x + 11y=-3$, we isolate $y$. First, subtract $4x$ from both sides: $11y=-4x - 3$. Then divide by 11: $y =-\frac{4}{11}x-\frac{3}{11}$.

Step2: Rearrange second equation for y

Starting with $-8x - 22y = 6$, first add $8x$ to both sides: $-22y=8x + 6$. Then divide by $-22$: $y=-\frac{8}{22}x-\frac{6}{22}=-\frac{4}{11}x-\frac{3}{11}$.

Step3: Classify the system

Since the two equations in slope - intercept form are identical ($y =-\frac{4}{11}x-\frac{3}{11}$ for both), the system has infinitely many solutions, so it is consistent - dependent.

Answer:

In slope - intercept form, the first equation is $y =-\frac{4}{11}x-\frac{3}{11}$
In slope - intercept form, the second equation is $y =-\frac{4}{11}x-\frac{3}{11}$
The system is Consistent - dependent