This is the equation of a line. There are an infinite number of solutions. All of the solutions are ordered pairs, (x,y) which represent points on that line.
For example take x=0 and y=7 so (0,7) is on the line.
Now take y=0 and x=7/3 is on the line. So the point (7/3,0) is on the lines.
Those two points are intercepts. If you graph them, you can connect them and you have a graph of the line.
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3x+7=37 -7 -7 3x=30 /3 /3 x=10
3x = 7 - 4x 3x + 4x = 7 - 4x + 4x 7x = 7 7x/7 = 7/7 x = 1
if 3x+5=x+19 then x=7
x = 7 and 2/3
(5, 1)