Question

Which graph shows the solution to the system of linear inequalities x-4y< 4 y < x+1

Answer 1

Answer:

Third graph in the image attached

Step-by-step explanation:

Let's rewrite the first inequality:

x - 4y < 4

-4y < 4 - x

4y > x - 4

y > x/4 - 1

We can draw the line y = x/4 - 1, then all values above this line will be solution for this inequality (check first graph in the image attached)

Now, for the second inequality, we have:

y < x+1

We can draw the line y = x + 1, then all values below this line will be solution for this inequality (check second graph in the image attached)

Now, if we combine these solutions, we have the third graph in the image attached.

The crossing point can be found making the value of y from one line equal the value of y from the other line:

$x/4 - 1 = x + 1$

$x - x/4 = -2$

$3x/4 = -2$

$3x = -8$

$x = -8/3$

$y = x + 1 = -5/3$

The crossing point is (-8/3 , -5/3)

Answer 2

Answer:

c

Step-by-step explanation: