#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]}
