How do you solve the system of equations #10x - 8y = 5# and #15x - 12y = 1#?

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Answer 1 · 2018-06-23T12:55:10

See a solution process below:

First, multiply the first equation by #color(red)(3)#:

#color(red)(3)(10x - 8y) = color(red)(3) xx 5#

#(color(red)(3) xx 10x) - (color(red)(3) xx 8y) = 15#

#30x - 24y = 15#

Next, multiply the second equation by #color(red)(2)#:

#color(red)(2)(15x - 12y) = color(red)(2) xx 1#

#(color(red)(2) xx 15x) - (color(red)(2) xx 12y) = 2#

#30x - 24y = 2#

The left side of both equations are equal: #30x - 24y#

However, the right side of both equations are not equal: #15 ~= 2#

This indicates the two lines are parallel lines and not the same line.

Therefore, there are no solutions or, in other words, the solution is the null or empty set: #{O/}#