Question 228486
How do you solve this by elimination?


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


Step 1.  Add Equations A and B


{{{x+2x+y-y=2+(-5)}}}


{{{3x=-3}}}


Step 2.  Divide by 3 to both sides of the equation


{{{3x/3=-3/3}}}


{{{x=-1}}}


Step 3.  Now substitute {{{x=-1}}} to either Equations A and B to find y.  Let's  substitute into Equation A.


{{{x+y=2}}} 


{{{-1+y=2}}}


Step 4.  Add 1 to both sides of the equation


{{{-1+y=1=2+1}}}


{{{y=3}}}


Step 5.  As a check see if {{{x=-1}}} and {{{y=3}}} satisfies Equation B {{{2x-y=-5}}}  


{{{2*(-1)-3=-5}}}


{{{-5=-5}}} which is a true statement and so {{{x=-1}}} and {{{y=3}}} satisfies both Equations A and B.


Step 6.  ANSWER:  The solution is {{{x=-1}}} and {{{y=3}}}.  This is the intersection point (-1,3) between the two lines.


Here's a graph of the two equations and note the intersection point at (-1,3)


{{{graph(400, 400, -10,10, -10, 10, -x+2, 2x+5)}}}


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