Question 216281
find the intersection of these two lines...


{{{3x=2+4y}}}  Equation A
{{{2y=6-5x}}}  Equation B


Step 1.  Let's put the variable terms x and y on the left side and numbers on the right side of equation as given by Step 2.


Step 2.  For Equation A, subtract 4y to both sides of the equation and; for equation B add 5x to both sides of the equation.


{{{3x-4y=2+4y-4y=2}}}  Equation A-1
{{{5x+2y=6-5x+5x=6}}}  Equation B-1


Step 3.  Multiply 2 to both sides of Equation B-1 to get {{{10x+4y=12}}}



{{{3x-4y=2}}}  Equation A-1
{{{10x+4y=12}}}  Equation B-2


Step 4.  Add Equations A-1 and B-2 and note the y-terms cancel each other out leaving the x-terms on the left side.


{{{3x-4y+10x+4y=2+12}}} 


{{{13x=14}}} or {{{x=14/13}}}


Step 5.  Substitute this value of x into either Equations A-1 or B-2.  Let's choose Equation A-1.

{{{3x-4y=2}}}  Equation A-1


{{{3*14/13-4y=2}}}


Multiply by 13 to both sides of equation to get rid of denominator


{{{42-4*13y=2*13}}}


{{{42-52y=26}}}


Add 52y-26 to both sides of equation


{{{42-52y+52y-26=26+52y-26}}}


{{{16=52y}}}


Divide 52 to both sides of the equation


{{{16/52=52y/52}}}


{{{y=4/13}}}


Step 6.  ANSWER:  So x=14/13 and y=4/13 or the intersection point is (14/13,4/13).


We can verify the above result by substituting these values into both equations to see if it leads to a true statement.


Here's another approach to solving the linear system equations by substitution:


*[invoke linear_substitution "x", "y", 3, -4, 2, 5, 2, 6 ]


Same result as before.


I hope the above steps were helpful.


For FREE Step-By-Step videos in Introduction to Algebra, please visit 

http://www.FreedomUniversity.TV/courses/IntroAlgebra and for Trigonometry visit 

http://www.FreedomUniversity.TV/courses/Trigonometry.


Good luck in your studies!


Respectfully,
Dr J