y = 2x + 1 and 3x + y = 11
We have two equations. Our job is to find the one pair of numbers — an x and a y — that makes both of them true at the same time.
Here's the first equation: y equals two x plus one.
And here's the second: three x plus y equals eleven.
Look — in the first equation, y is already alone. That makes substitution easy.
Wherever we see y in the second equation, we can replace it with two x plus one.
Now combine like terms. Three x plus two x is five x, so we get five x plus one equals eleven.
Subtract one from both sides. Five x equals ten.
Divide both sides by five. x equals two!
Now plug x equals two back into the first equation to find y.
Two times two is four, plus one is five. So y equals five.
Our solution is the point two, five — the one pair that makes both equations true. Nice work!