Let's plot the lines to see how their graph look like:
for the first equation, we have:
7x + y = 3, at x equals 0, we get:
7*0 + y = 3
y = 3, then the first line goes through the point (0,3)
At x equals 1, we get:
7*1+y=3
y = 3-7= -4
Then, the first line goes through the points (0, 3) and (1, -4).
For the second equation, taking the same values of x, we get:
y = -7*0 + 10 = 10 (0, 10)
y= -7*1 +10 = 3 (1, 3)
Now that we know two points of the lines, let's graph them:
As you can see, are not the same, the lines are parallel, which means that they don't intersect and that's why this system has no solution not even at point (0,0)
