Question 1161340

An equation {{{ax + bx = 8}}} -> you have {{{bx}}} and it should be {{{by}}}

passing through lines ({{{3}}},{{{-2}}}) and ({{{2}}},{{{4}}}). 

Find the values of {{{a}}} and {{{b}}}!

{{{ax + by = 8}}}....use point ({{{3}}},{{{-2}}}) 


{{{3a -2b = 8}}}.....solve for {{{a}}}

{{{3a = 2b+8}}}

{{{a = 2b/3+8/3}}}.....eq.1


{{{ax + by = 8}}}....use point ({{{2}}},{{{4}}})

{{{2a + 4b = 8}}}

{{{2a = 8-4b}}}

{{{a = 4-2b}}}......eq.2


from eq.1 and eq.2 we have


{{{ 2b/3+8/3=4-2b}}}.....solve for {{{b}}}


{{{ 2b/3+2b=4-8/3}}}....both sides multiply by {{{3}}}


{{{ 2b+6b=12-8}}}

{{{ 8b=4}}}

{{{ b=4/8}}}

{{{ b=1/2}}}


go to

{{{a = 4-2b}}}......eq.2, substitute {{{b}}}

{{{a = 4-2(1/2)}}}

{{{a = 4-1}}}

{{{a = 3}}}

and, your equation is:

{{{3x + (1/2)y = 8}}}


{{{ drawing ( 600, 600, -10, 10, -10, 10,
circle(2,4,.12),locate(2,4,p(2,4)),
circle(3,-2,.12),locate(3,-2,p(3,-2)),
graph( 600, 600, -10, 10, -10, 10, -6x+16)) }}}