-4.5x-2y=-12.5 solve by substitution

Question

im trying to figure this out

Answer 1

In order to solve by substitution the first step is to isolate one variable.  Either one works, but sometimes there is one that is already isolated or just easier to access.  In this case let's choose X for no reason other then math problems usually revolve around X.

 

-4.5x-2y=-12.5

(add 2y to both sides)

-4.5x =-12.5+2y

(divide both sides by -4.5)

x=(-12.5/-4.5)+(2y/-4.5)

 

Unfortunately the fractions do not simplify to whole numbers, but we have solved for X.  The next step, now that we have a solution for X, is to substitute that solution for X in the original problem, which will leave everything in terms of Y, thus letting us find the value of Y.

 

(original once more)

-4.5x-2y=-12.5

(substitute in equation for x)

-4.5((-12.5/-4.5)+(2y/-4.5))-2y=-12.5

 

It looks a little messy, but with a little work we can evaluate it.  This is usually the hardest part, and the most important thing is to make sure to distribute properly and not make an mistakes with sign changes (+,-)

 

-4.5((-12.5/-4.5)+(2y/-4.5))-2y=-12.5

(distribute -4.5 across the parentheses.  This works very well because that cancels out the denominator)

(-4.5*-12.5/-4.5)+(-4.5*2y/-4.5)-2y=-12.5

(-12.5)+(2y)-2y=-12.5

(now we can try to simplify further)

(add 12.5 to both sides)

2y-2y=0

(simplify)

0=0

 

What this means is that there is an infinite number of solutions to this problem.  For any X value, there can be a Y value that is correct, as well as for any Y value there is an X value that is correct.

 

On an added note, the result this time was TRUE because 0=0 is a true statement, but if the result had been FALSE such as 0=7 it would mean that there are no real solutions that would solve the problem.

 

If there was another equation then it is possible that there would be only 1 solution, where the lines represented by both equations intercepted.

 

I hope this helps and makes sense, and if there are any questions just let me know :)

 

Thank you very much,

 

Blue

Answer 2

Given;

 

-4.5x - 2y = -12.5

 

Using substitution, lets start by solving for 'y';

 

multiply the equation by -1

 

-1(-4.5x - 2y = -12.5)

 

that would give;

 

4.5x + 2y = 12.5

 

2y = 12.5 - 4.5x

 

y = (12.5 - 4.5x)/2

 

y = 6.25 - 2.25x

 

Now Sub the value of y into the original equation.

 

-4.5x - 2y = -12.5

 

-4.5x - 2(6.25 - 2.25x) = -12.5

 

-4.5x - 12.5 + 4.5x = -12.5

 

-4.5x + 4.5x = -12.5 + 12.5

 0 = 0

 

The Equation cannot be solved using substitution.

Cheers!