What is the soulution to the system of equations: 5y-x=3; x-5y= -3?

Question

There is no description. My teacher doesn't know how to tech so im asking you for help

Answer 1

Hi Zoey, I am in your area, so if you ever need help with math I am available for tutoring!

 

With that being said, the easiest way to solve a system of equations is through substitution. This would mean that you solve for one of the variables in one of the equations (x=...  or y=... ), and then you would substitute that variable right into the second equation wherever it says "x" or "y" (whichever one you solved for). Then you just have one variable in the second equation.

 

The other way to solve a system is by adding the two equations together once you've multiplied by a constant. The purpose of this is to cancel out one of the variables. But that is a little more complex, and we don't need to do that here.

 

You can see that these two equations represent the same line, if you solve them both for x:

 

1. 5y-x=3   =>  x=5y-3

2. x-5y=-3  =>  x=5y-3

 

They are the same line!  Therefore, the solution to this system is any point (x,y) that lies on this line.

 

Hope this helps!

Answer 2

-x + 5y = 3           eq1

x - 5y = -3            eq2

 

 

We want to find the value of x and y that will satisfy both equations.  There are two ways we can do this. 

 

1) Substitute one equation into another

2) Use elimination method by multiplying the equations by a certain number, and then adding or subtracting the equations to eliminate either the x terms or y terms. 

 

These methods both allow us to get to one equation with one variable, since it is difficult to solve an equation that has two different variables.  I intend to show you both.

 

 

Substitution method:

 

From eq2,

 

x = 5y - 3

 

Substitute this value of x into eq1.  This will allow us to have eq1 in terms of y only and we only have one equation to work with.

 

-(5y - 3) + 5y = 3

 

-5y + 3 + 5y = 3

 

Notice that -5y and 5y cancel each other out.  The equation now becomes 3 = 3.

 

We could not solve for y, but the end result turned out to be true. 

 

 

Elimination method:

 

 

If we add the equations together, we obtain

 

0x + 0y = 0

 

We could not solve for either x nor y, but the equation is true.  0 times x is 0.  0 times y is 0.  0 + 0 = 0.  This is true also.

 

 

Now, I would like to show you a visual method.  The graphical method.  We graph these equations on the same coordinate system.  First, we need to write each of the given equations in slope-intercept form.

 

 

Eq1

 

5y = x + 3   --->   y = (1/5)x + 3/5

 

 

Eq2

 

-5y = -x - 3  --->   y = (1/5)x + 3/5

 

 

Notice that these equations are the same line.  This means that the solution is infinite.  The other methods mentioned above also show this.

 

 

Answer 3

You are given two equations and two variables. Therefore, it is possible to solve for both of these questions by setting them equal in some way, shape, or form. 

 

Go ahead and make things simple for yourself and manipulate both of the equations to equal the 'y' variable. I will input the first equation that you wrote as y1 and the second as y2. 

Therefore:

 

y1=(3+x)/(5)

y2=(-3+x)/(-5)

 

So, in this form, you can see that the equations are different only by sign changes. Now, simply graph the two equations using a graphing calculator and find the intersection point between the two. 

 

The answer should be. y=3/5 x=0

 

Plug these answers back into your original equations to check. 

 

Answer 4

To expand a bit on Nathan's answer.........  since these represent the same line, there are infinitely many solutions.  For example (2,1), (7,2), (12,3).  By solving one of the equations for "y" you can determine the relationship between x and y; y=(3+x)/5.

 

Hope this helps a bit further.

Answer 5

5y - x = 3

x - 5y = -3

 

What we have here is a pair of linear equations. The first step is to isolate our y values in each:

5y - x = 3  (first we add x to both side)

5y = x + 3 (now we divide both sides by 5)

y = 1/5 x + 3

 

x - 5y = -3 (first we subtract x from both sides)

-5y = -x - 3 (now we divide both sides by -5)

y = 1/5 x + 3

 

If we take a look at both of these problems, they both have a slope of 1/5, and their b-values are the same, being 3. That means these two linear equations are the same--no matter what we put in for x, our y will be the same for both.

 

If you wanted to try the elimination method for further evidence, we have:

 5y -  x =  3
-5y + x = -3

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 0 + 0 = 0 Both equations are equal to one another.