How do you solve the system of equations #3x - 9y = 5# and #- 15x + 45y = - 30#?

1 Answer
Apr 22, 2017

See the entire solution process below:

Explanation:

Step 1) Solve the second equation for #x#:

#-15x + 45y = -30#

#-15x + 45y - color(red)(45y) = -30 - color(red)(45y)#

#-15x + 0 = -30 - 45y#

#-15x = -30 - 45y#

#(-15x)/color(red)(-15) = (-30 - 45y)/color(red)(-15)#

#(-15x)/color(red)(-15) = (-30)/color(red)(-15) - (45y)/color(red)(-15)#

#(color(red)(cancel(color(black)(-15)))x)/cancel(color(red)(-15)) = 2 - (-3y)#

#x = 2 + 3y#

Step 2) Substitute #2 + 3y# for #x# in the first equation and solve for #y#:

#3x - 9y = 5# becomes:

#3(2 + 3y) - 9y = 5#

#(3 * 2) + (3 * 3y) - 9y = 5#

#6 + 9y - 9y = 5#

#6 + 0 != 5#

#6 != 5#

This problem has no solution which means the lines represented by this equation are parallel lines, and are not the same lines. Therefore, there is no point where they intersect.