How do you solve the system of equations #4y = 9x - 17# and #9x - 6y = 3#?

1 Answer
Mar 24, 2018

Answer:

#x=5 and y=7#

Explanation:

Both equations have the same term in #x#.

To eliminate the #x# term, you could subtract the equations,
However, here is another option:

Isolate the #9x# term in each equation.

#color(blue)(9x = 6y+3)" " and" "color(red)(9x =4y+17#

#color(white)(wwwwwwwww.)color(blue)(9x) =color(red)(9x)#

therefore the two right hand sides are also equal

Equate them: #" "color(blue)(6y+3) = color(red)(4y+17#

#color(white)(wwwwwwwww.)6y-4y =17-3#

#color(white)(wwwwwww.wwww.)2y = 14#

#color(white)(w.......www.wwwww.)y=7#

Substitute #7# for #y# to find the value of #x#

#color(white)(wwwwwwwww.)9x = 6(7) +3#

#color(white)(wwwwwwwww.)9x = 45#

#color(white)(wwwwwww.ww.)x =5#