How do you solve the system of equations #-x+7y=3# and #-4x+28y=12# by the elimination method?

1 Answer
Feb 24, 2017

Answer:

Infinite solutions.

Explanation:

If we multiply #-x+7y=3# by #4# it leads to

#-4x+28y=12#, the same as the second equation.

Hence #-x+7y=3# and #-4x+28y=12# represent same line

or two coinciding lines.

Now as #-x+7y=3# leads to #x=7y-3#, any point #(7k-3,k)# falls on these lines and hence the sets of equation has infinite solutions as putting any value of #k# will give a solution to 'two' equations.

Elimination method

Trying elimination method we have obtained #x=7y-3# from first equation and putting this in second eliminates #x# and we get

#-4(7y-3)+28y=12#

or #-4xx7y-4xx(-3)+28y=12#

or #-28y+12+28y=12#

or #12=12#

When we have such pair of equations, as may be observed, we find that other variable too is eliminated and we get #a=a#, where #a# is a real number (here #a=12#). This denotes 'two' coinciding lines (when graphed) and infinite solutions.

Note - if we get two unequal numbers #a=b#, where #a# and #b# are two different numbers, this means two parallel lines. For example one can try for #-x+7y=8# and #-4x+28y=12#.