color(red)(-2x)+5y=13to(1)
color(red)(16x)+3y=25to(2)
color(blue)"solving by elimination" means attempting to eliminate one of the variables x or y from an equation leaving the equation with only one variable which we can solve.
"note that multiplying " color(red)(-2x)" in (1) by 8 gives"
color(red)(-16x)" and adding it to " color(red)(16x)" in (2) will "
color(blue)"eliminate"" the x-term"
"multiply ALL terms in " (1)" by 8"
rArrcolor(red)(-16x)+40y=104to(3)
"adding equations " (2)" and " (3)" term by term gives"
(16x-16x)+(3y+40y)=(25+104)
rArr43y=129larrcolor(red)" variable x is eliminated"
"divide both sides by 43"
(cancel(43) y)/cancel(43)=129/43
rArry=3
"substitute this value in either " (1)" or " (2)
16x+9=25larr" substituting in " (2)
"subtract 9 from both sides"
16xcancel(+9)cancel(-9)=25-9
rArr16x=16rArrx=1
(1,3)" is the point of intersection of the 2 linear equations" graph{(y-2/5x-13/5)(y+16/3x-25/3)=0 [-10, 10, -5, 5]}
