SOLUTION: I need help with this one: Find the common solution to the following pair of lines by graphing them on the same axes. 4x + y = 1 y = x + 6 The lines intersect at (?,? ).

Get some points on the first line:

 x  |  y
-2  |  9
 0  |  1
 1  | -3

 

Get a ruler and draw a straight line through those three points,
like the green line below:



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Get some points on the second line:

 x  |  y
-3  |  3
 0  |  6
 1  |  7


Get a ruler and draw a straight line through those three points,
like the blue line below:



From the point where those lines cross, draw a line segment
perpendicular to the x-axis, and another perpendicular to the
y-axis (the two black line segments below:



Notice that the vertical black line segment touches the x-axis at -1,
and the horizontal black line segment touches the y-axis at 5.

The lines intersect at (-1,5). 

Therefore the solution is x=-1 and y=5.  The solution is
often written (x,y) = (-1,5).

To check, we substitute -1 for x and 5 for y in both original equations:



Substituting in the first:






That is an identity.  

Substituting in the second:






That is also an identity, so we have found the common
solution to those two equations.

Edwin