I can't remember how to graph this to answer the question. what is the solution of the system of equations?
5x-5y=35
5y-5x=-35
Consistent or inconsistent?
Dependent or independent?
Thank you

Question

I can't remember how to graph this to answer the question.  what is the solution of the system of equations?
5x-5y=35
5y-5x=-35
Consistent or inconsistent?
Dependent or independent?
Thank you

anonymous · Answer

The equations are saying the same thing. Note that if you multiply either equation by -1 you will get the other. Therefore they are consistent, but they are also dependent. Every point on that line is a solution.

anonymous · Answer

Thank you
Is it a rule to multiply by 1 to get the solution for problems like these?

anonymous · Answer

So the equation has infinitely many solutions?

anonymous · Answer

The equation has infinitely many solutions yes. The way to get solutions is typically to add multiples of the equations to eliminate one variable then solve for the other variable.

e.g.

2x+3y = 5 (eq1)
4x + y = 2 (eq2)

We see that
$$-2*(eq1) \implies -2(2x+3y) = -2(5)\implies -4x -6y = -10$$

     4x +y  = 2        (eq2)
+ -4x-6y = -10    -2(eq1)
==========
          -5y = -8        $\implies  y=8/5$

Then we plug back in to find x
$$4x+y = 2 \implies 4x + 8/5 = 2 \implies 20x + 8 = 10$$
$$\implies 20x = 2 \implies x = 1/10$$