SOLUTION: Graph the 2 lines below; and from the graph, read off the point of intersection. y=2x+3 y=x+5

Get 3 points on the first line:

Arbitrarily select, say, x = 0 and substitute 0 for x in the
first equation:






So the first point on the first line is (x,y) = (0,3)

---

Arbitrarily select, say, x = -2 and substitute -2 for x in the
first equation:






So the second point on the first line is (x,y) = (-1,-1)

---

Arbitrarily select, say, x = 3 and substitute 3 for x in the
first equation:






So the third point of the first line is (x,y) = (3,9)

Plot those three points:



Get a ruler and draw a straight line through them:



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Get 3 points on the second line:

Arbitrarily select, say, x = 1 and substitute 1 for x in the
second equation:






So the first point on the second line is (x,y) = (1,6)

---

Arbitrarily select, say, x = -1 and substitute -1 for x in the
second equation:






So the second point on the second line is (x,y) = (-1,4)

---

Arbitrarily select, say, x = 4 and substitute 4 for x in the
second equation:






So the third point of the second line is (x,y) = (4,9)

Plot those three points:



Take your ruler and draw a straight line through
those three points:



Now take your ruler and draw 2 lines from the point
where the two lines cross, one directly to the x-axis
and one directly to the y-axis:



Notice that these last two lines hit the x-axis
at 2 and the y-axis at 7.  So the solution is

, , sometimes written

(x,y) = (2,7)

To check we substitute  and 
in both equations:






It checks the first equation.  Now let's see if
it checks the second equation.





So it checks both equations, so it is correct.

Edwin