Two Lines, One Answer

A system asks us to satisfy two or more equations at the same time. Here, both equations are linear, so their graphs are straight lines. A point satisfying both equations lies on both lines. If the lines intersect once, that intersection is the system's only solution.

The crossing (1, 2) solves both equations at once

Check $\left(1, 2\right)$ by substituting into both equations. In $y = x+1$, we get $2 = 1+1$. In $y = -x+3$, we get $2 = -1+3$. Both are true, so the point solves the system.