Final answer:
The solution to the system of inequalities by substitution is y ≤ 9 and x ≤ -10, which represents all points (x, y) in the coordinate plane satisfying these conditions.
Step-by-step explanation:
To solve by substitution, we begin with the system of inequalities 2x + 3y ≤ 7 and 2y ≥ x + 28. First, solve one of the inequalities for one variable, then substitute that expression into the other inequality. Let's choose to solve the second inequality for x.
x ≤ 2y - 28.
Now, substitute this expression for x in the first inequality:
2(2y - 28) + 3y ≤ 7.
Simplify and solve for y:
4y - 56 + 3y ≤ 7,
7y ≤ 63,
y ≤ 9.
Next, substitute y ≤ 9 into the first expression we found for x:
x ≤ 2(9) - 28,
x ≤ 18 - 28,
x ≤ -10.
Thus, the solution set consists of all points (x, y) such that y is less than or equal to 9 and x is less than or equal to -10,