Another way to check the solution is to replace x and y with the coordinates of the point of intersection. So you'll replace x with 1 and y with 4. The idea is that after the replacements, it should lead to a true equation.
So in the first equation we have -3x+y = 1
Replace x and y with 1 and 4 respectively to get -3(1)+4 = 1
The left side -3(1)+4 simplifies to 1. Therefore -3(1)+4 = 1 turns into 1 = 1
We have a true equation, so the point (x,y) = (1,4) confirms the first equation. We'll follow similar steps for the second equation as well
4x+y = 8 .... second equation
4(1)+4 = 8 ... replace x and y with 1 and 4
4+4 = 8
8 = 8 ... true equation
Since both equations of the system are true when (x,y) = (1,4) this means this point is on both lines at the same time. Hence, it is at the intersection point. This is an algebraic way to confirm the solution.
