Question 223154
How do you solve this equation by graphing 


x-y=3
x+y=5


Step 1.  Plot the above equation using the slope intercept form given as y=mx+b where m is the slope and b is the y-intercept when x=0 or at point (0,b).


Step 2. Put x-y=3 in slope intercept form or y=x-3 where we added y-3 to both sides of the equation.  Here the slope m=1 and b=-3.   


Step 3.  Put x+y=5 in slope intercept form where y=-x+5 where we added -x to both sides of the equation.  Here the slope is m=-1 and b=5.


{{{graph(400,400,-5,5,-5,5, x-3, -x+5)}}}


Step 4.  ANSWER:  Based on the above graph, the two lines intersect at point (4,1) or x=4 and y=1.


We can check by substituting in the original equations:


{{{x-y=3}}} or {{{4-1=3}}}  which is a true statement


{{{x+y=5}}} or {{{4+1=5}}} which is also a true statement.  


So the point (4,1) is a solution to the system of equations.


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J