Question 214304
Find the intersection of the following pairs of lines.


f(x)=3x+8, g(x)=6x+1


He does not want the composition answer. Please help me.


Step 1.  We can write the above equations as


{{{y=3x+8}}}


{{{y=6x+1}}}


Step 2.  Since these two lines intersect they save the same y or


{{{3x+8=6x+1}}}


Step 3  Add -3x-1 from both sides of equation to get only x-terms on the right side and only numbers on the left side.


{{{3x+8+(-3)x-1=6x+1+(-3)x-1}}}


{{{7=3x}}}


Step 4.  Divide by 3 to both sides of the equations.


{{{7/3=3x/3}}}


{{{7/3=x}}} or {{{x=7/3}}}


Step 5.  Now substitute x=7/3 into above equations and it should yield the same y.


{{{y=3x+8=3*(7/3)+8=7+8=15}}}


{{{y=6x+1=6*(7/3)+1=14+1=15}}}


and y=15 for both equations


Step 6.  ANSWER:  The intersection point is (7/3, 15)


A graph of the lines is shown below and note the intersection point.


{{{graph(400,400, -5, 5, -25, 25, 3x+8, 6x+1)}}}


I hope the above steps were helpful. 


For free Step-By-Step Videos on Introduction to Algebra, please visit http://www.FreedomUniversity.TV/courses/IntroAlgebra or for Trigonometry visit http://www.FreedomUniversity.TV/courses/Trigonometry.


And good luck in your studies!


Respectfully,
Dr J