Question 227843
{{{x + y = 7}}}  Equation A
{{{x + 3y = 11}}}  Equation B


Step 1.  Subtract Equation A from Equation B (or Equation B - Equation A) to eliminate x


{{{x-x+3y-y=11-7}}}


{{{2y=4}}}


Step 2.  Divide by 2 to both sides of the equation


{{{2y/2=4/2}}}


{{{y=2}}}


Step 3.  Now Substitute {{{y=2}}} into equation A {{{x + y = 7}}} to find x


{{{x+2=7}}}


Subtract 2 from both sides to get x.


{{{x+2-2=7-2}}}


{{{x=5}}}


Step 4.  Now we have {{{x=5}}} and {{{y=2}}} as a solution.  Check to see if this also satisfies equation B  {{{x + 3y = 11}}}.


{{{5+3*2=11}}}


{{{11=11}}}  which is a true statement


Step 5.  ANSWER:  The solution is {{{x=5}}} and {{{y=2}}}.  Or the intersection point between these two lines is (5,2).  See graph below,


{{{graph(400,400, -10, 10, -10, 10, -x+7, -x/3+11/3)}}}


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


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