Let's solve the linear equation two y plus three equals eleven. We need to isolate the variable y by performing algebraic operations on both sides of the equation.
Step one: subtract three from both sides. We start with two y plus three equals eleven. Subtracting three from both sides gives us two y plus three minus three equals eleven minus three, which simplifies to two y equals eight.
Step two: divide both sides by two. We have two y equals eight. To isolate y, we divide both sides by two. This gives us two y divided by two equals eight divided by two, which simplifies to y equals four.
Let's verify our answer. We substitute y equals four back into the original equation. Two times four plus three equals eleven. This gives us eight plus three equals eleven, which is eleven equals eleven. Our answer is correct.
To summarize: we successfully solved the linear equation two y plus three equals eleven. We used two algebraic steps: first subtracting three from both sides, then dividing by two. Our final answer is y equals four, which we verified by substitution.