a) \( x+y=5 ; \quad x-y=3 \)

To solve these equations, we can use the substitution or elimination method. Let’s use elimination here. Adding both equations together eliminates \(y\): \[ (x + y) + (x - y) = 5 + 3 \] This simplifies to \(2x = 8\), giving us \(x = 4\). Now, substituting \(x = 4\) back into the first equation: \[ 4 + y = 5 \] This leads to \(y = 1\). So the solution is \(x = 4\) and \(y = 1\). Now, if you were to visualize this, you could graph both equations. The intersection point where both lines cross is where your solution lies! In our case, it would be the point (4, 1), giving a lovely geometric representation of the algebra we just solved.