the ordered pair that is a solution to the system of inequalities = (1,3)
Explanation:
The given inequalities:
y > -2
x + y ≤ 4
We need to find a solution that satisfy both inequalites. In other word,s the solution must appear in the two inequalities solution set - It has to overlap.
y > -4
This means for this inequality y is greater than -4
x + y ≤ 4
Making y the subject of formula:
y ≤ 4 - x
Recal linear function is in the form: y = mx + c
We can compare that to the inequality above: y ≤ -x + 4
m = slope = -1
intercept = c = 4 (this is the value that will be seen on y axis when the graph is plotted)
We can plot the graph by assuming values for x. Then we would get corresponding values of y
Let x = -2, -1, 0, 1, 2
To get y values, we remove the inequality and represent with the equal sign:
y = -x + 4
when x = -2,
y = -(-2) + 4 = 2+4 = 6
The corresponding y values: 6, 5, 4, 3, 2
The plotted graph: The 1st represent (y>-2), the second consist of both inequalities
The part that overlaps is the solution of the inequalites: It has both the red and blue colour overlapping.
To determine which of the options is an ordered pair, we need to check the options and compare with numbers that fall in the overlapped region for (x, y) coordinate on the graph
a) (1, 3) falls in the region: When x= 1, y = 3. Each line represents 2units. the middle of the line represent 1 unit (2+1 = 3unit).
b) (-2, 3) doesn't fall in the region: When you trace, x = 2 falls in the region, but y = -3 didn't
c) (1, -5) doesn't: when x= 1, y= 5 doesn't fall in the region
d) (0, -4) doesn't: when x = 0 (this falls in the region), y = -4 doesn't fall in the region
Hence, the ordered pair that is a solution to the system of inequalities = (1,3)
