How do you solve the system 5x - y = 3 and -10x + 2y = -6?

1 Answer
Jun 30, 2017

Answer:

See a solution process below:

Explanation:

Both of these equations are almost in the Standard Form for linear equations. The standard form of a linear equation is: #color(red)(A)x + color(blue)(B)y = color(green)(C)#

Where, if at all possible, #color(red)(A)#, #color(blue)(B)#, and #color(green)(C)#are integers, and A is non-negative, and, A, B, and C have no common factors other than 1.

We can get the second equation closer to Standard Form by multiplying both sides of the equation by #-1#:

#-1(-10x + 2y) = -1 * -6#

#10x - 2y = 6#

Now, we can divide each side of the equation by #2# to get this equation into true standard form:

#(10x - 2y)/2 = 6/2#

#5x - y = 3#

These equations are actually the same equation. Therefore, the solution to this is they have all points in common.