-7x+4y>+=-28 and 2x+10y> 20 intersect
To determine the intersection point of the two inequalities -7x + 4y ≥ -28 and 2x + 10y > 20, we first need to find the equations of their corresponding boundary lines.
For -7x + 4y ≥ -28:
1. Replace the inequality sign with an equal sign to obtain the equation: -7x + 4y = -28.
2. Rearrange the equation to solve for y: 4y = 7x - 28 ⇒ y = (7/4)x - 7.
For 2x + 10y > 20:
1. Replace the inequality sign with an equal sign to obtain the equation: 2x + 10y = 20.
2. Rearrange the equation to solve for y: 10y = -2x + 20 ⇒ y = (-2/10)x + 2 ⇒ y = (-1/5)x + 2.
Now that we have the equations of the boundary lines, we can graph them on a coordinate plane:
-7 | .
-6 | .
-5 | . .
-4 | .
-3 | .
-2 | .
-1 | .
0 | .
1 | .
2 |
-7x + 4y = -28
-1 0 1 2 3
-|
-|
-|
-|
-| .
-|
-| .
-| .
-| .
-| .
_|__________________
y = (7/4)x - 7
On the same graph, we can now add the second boundary line:
-7 | .
-6 | .
-5 | . .
-4 | .
-3 | .
-2 | .
-1 | .
0 | .
1 | .
2 |
-7x + 4y = -28
-1 0 1 2 3
-|
-|
-|
-|
-| .
-|
-| .
-| .
-| .
-| .
_|__________________
y = (7/4)x - 7
.
.
.
.
y = (-1/5)x + 2
Now, we observe the intersection point(s) of the two lines. The solution to the system of inequalities is the region bounded by the shaded area where both inequalities are satisfied.