Question 417848
substitution method

(a)

{{{y=x-7}}} .....1..substitute {{{y}}} in  2  
  
{{{3x-y=-1}}}...2       

{{{3x-(x-7)=-1}}}

{{{3x-x+7=-1}}}

{{{2x=-1-7}}}

{{{2x=-8}}

{{{x=-4}}...now find {{{x}}}

{{{y=-4-7}}}

{{{y=-11}}}


check:

{{{-11=-4-7}}} .....1

{{{-11=-11}}}


(b) 

{{{3x+7y=5}}}.....1

{{{ x+4y=5}}}.....2.solve for {{{x}}}

{{{ x=-4y+5}}}.plug in 1

{{{3(-4y+5)+7y=5}}}.....1.solve for {{{y}}}

{{{-12y+15+7y=5}}}

{{{-5y=5-15}}}


{{{-5y=-10}}}

{{{y=2}}}............find {{{x}}}

{{{ x=-4*2+5}}}

{{{ x=-8+5}}}

{{{ x=-3}}}


check:

{{{3(-3)+7*2=5}}}.....1

{{{-9+14=5}}}

{{{5=5}}}


solve using elimination

{{{3x+2y=19}}}

{{{x-2y=3}}}.....add both 
--------------------

{{{3x+x+2y-2y=19+3}}}


{{{3x+x+cross(2y)-cross(2y)=19+3}}}


{{{4x=22}}}

{{{x=22/4}}}

{{{x=5.5}}}......find {{{y}}}


{{{3*5.5+2y=19}}}


{{{16.5+2y=19}}}

{{{2y=19-16.5}}}

{{{2y=2.5}}}

{{{y=2.5/2}}}

{{{y=1.25}}}



check:

{{{3*5.5+2*1.25=19}}}

{{{16.5+2.5=19}}}

{{{19=19}}}