The solution to the system of inequalities is 5 < y < 1
Given the inequality
3y + 9 <4y + 7
Collect the like terms
3y - 4y < 7 - 9
-y < -2
Divide both sides by -2
-2y/-2 < -2/-2
y < 1
Similarly for the expression 7y - 2(y - 4) > - 2y + 43
Expand
7y - 2y + 8 > - 2y + 43
5y + 8 > -2y + 43
Collect the like terms
5y + 2y > 43 - 8
7y > 35
y > 35/7
y>5
5 < y
Combine both inequality expressions
5 < y < 1
Hence the solution to the system of inequalities is 5 < y < 1
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