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: ${O/}$

How do you solve the system of equations 10x - 8y = 510x - 8y = 5 and 15x - 12y = 115x - 12y = 1?