Question 244772
Solve using the substitution method. Show your work. If the system has no solution or an infinite number of solutions, state this.

1.
5x - 2 = y
y - 5x = 1

Substitute 5x-2 in for y in the second equation
so 
5x-2-5x=1
5x-5x is 0 so you are left with -2=1, since this is not true, then there is no solution.

2.
x=y+2/5
y-5(y+2/5)=1

y-5y+10/5=1  This should be {{{y-5y-10/2=1}}} because -5 is distributed to both terms (not -5 to the first term and +5 to the second term)  also, 10/2 is just 5, so the next step I will write it that way.

{{{-4y-2=1}}}  Combine y values
+2_______+2
{{{-4y=3}}}
y=-3/4   (divide both sides by -4)
so now insert this into x=y+2/5 to find x  {{{x=-3/4+2/5}}} get a common denominator and you get {{{x=-15/20+8/20=-7/20}}} 
check your answer by inserting these values into your original equations.

I have another one if you don't mind also
Solve using the elimination method. Show your work. If the system has no solution or an infinite number of solutions, state this.

-0.9x + 0.8y = 14.6
-0.3x + 0.1y = 3.7
Here is what I put as an answer 

-9x+8y=146
-3x+1y=37
__________
-9x+8y=146
+9x-3y=-111
____________
5y=35
________
5   5
y=7

-3x+7=37
-3x=30
x=-10
So y=7 and x=-10

Plug these in and check them