There are two variables, x and y, and only one equation, so it's not possible to solve for x if we're looking for an actual numerical value for x. But we can find x in terms of y, which means that, if we know or put in a value for y, we can find x:
23x+13y=-29, subtract 13y from each side of the equation:
23x=-29-13y, now divide both sides by 23:
x=(-29-13y)/23. This produces x in terms of y.
This equation is true for every possible value we can put in y.
For example, if y=0, x=-29/23; if y=1, x=-42/23; if y=42, x=-25. If you plotted these on a graph, (-29/23,0), (-42/23,1), (-25,42), you would get a straight line. All the points on this line (which is infinitely long) are solutions to the equation.