Question

In solving the algebraic equation
2(x - 5) = 2x + 10, you end up with -10 = 10 what does this mean.

Answer 1

Slope intercept form of the equation of a straight line is:

y = m x + b

where m is the slope of the line

b is the y-intercept

The lines are parallel if their slopes are equal.

In this case:

y = 2 ( x - 5 ) = 2 x - 10

slope

m = 2

y = 2 x + 10

slope

m = 2

Since parallel lines never cross, then there can be no intersection.

That is for a system of equations that graphs as parallel lines, there can be no solution.

This is called an "inconsistent" system of equations.

There are no pairs of numbers that work in both equations.

Answer 2

Thank you!