## since 5^4 = 625

and 3^(2x)*3^y = 3^(2x+y) and 243 = 3^5

x-y = 4

2x+y = 5

not so hard now, eh?

(note: I posted a similar question to this before, but this uses indices)

(Also note: Answer is, x = 3, y = -1 ; 7, and the question if inputted into an online calculator, is incorrect.)

Thnks for your time.

Steve
answered

6 years ago

6 years ago

and 3^(2x)*3^y = 3^(2x+y) and 243 = 3^5

x-y = 4

2x+y = 5

not so hard now, eh?

Anonymous
answered

6 years ago

6 years ago

Reiny
answered

6 years ago

6 years ago

https://www.jiskha.com/display.cgi?id=1511439208

btw, give yourself a nickname instead of "anonymous" to find your posts easier.

Anonymous
answered

6 years ago

6 years ago

Explain Bot
answered

1 year ago

1 year ago

Let's start with the first equation:

5^(x - y) = 625

Since 625 can be written as 5^4, we can rewrite the equation as:

5^(x - y) = 5^4

Now we can equate the exponents:

x - y = 4

Next, let's move on to the second equation:

3^(2x) * 3^y = 243

Since 243 can be written as 3^5, we can rewrite the equation as:

3^(2x) * 3^y = 3^5

Using the properties of exponents, we can add the exponents on the left side:

3^(2x + y) = 3^5

Now we can equate the exponents:

2x + y = 5

We have a system of two equations:

x - y = 4

2x + y = 5

To solve this system, we can use the method of substitution. Solve one equation for one variable and substitute it into the other equation.

From the first equation, we can solve for x:

x = 4 + y

Now substitute this expression for x into the second equation:

2(4 + y) + y = 5

Simplify the equation:

8 + 2y + y = 5

3y + 8 = 5

3y = 5 - 8

3y = -3

y = -1

Substitute the value of y back into the first equation to find x:

x - (-1) = 4

x + 1 = 4

x = 4 - 1

x = 3

Therefore, the solution to the given system of equations is:

x = 3

y = -1