3х - 30 = у
7y - 6 = 3х

Step-by-step explanation:

This one is simple substitution... at least, substitution is the easiest method. The first equation is 3x – 30 = y  and the second is 7y – 6 = 3x

As I look, I see 3 ways to use substitution to solve this:

We're going to only use 1 method for the sake of time. Try the other two on your own. Assuming you don't make any mistakes, they will work.

Method 1:

3x – 30 = y

7y – 6 = 3x  — initial system of equations

7y – 6 – 30 = y  — substitute 7y – 6 for 3x

7y – 6 – 30 = y  — marking like terms, bold for constants, underlined for variables

7y – 36 = y  — combining the constants and simplifying

Here, you could diverge into multiple paths: add 36 to both sides, subtract y from both sides, divide by 6 OR subtract 7y from both sides and divide by –6 . For the sake of time, I'm subtracting 7y, though I don't like dealing with negatives.

7y – 7y – 36 = y – 7y  — subtract 7y from both sides

–36 = –6y  — simplify

–36 ÷ –6 = –6y ÷ –6  — divide by –6 on both sides

y = 6  — simplify

Again, we can diverge here: substitute y into 3x – 30 = y or substitute y into 7y – 6 = 3x

I'm going to choose 3x – 30 = y but it will work either way, should you take the time (if you have it) to chase down every path this problem can take.

3x – 30 = y  — initial equation

3x – 30 = 6  — substitute 6 for y

3x – 30 + 30 = 6 + 30  — add 30 to both sides to isolate 3x

3x = 36  — simplify the expression

3x ÷ 3 = 36 ÷ 3  — divide both sides by 3 to isolate x

x = 12  — simplify

So, we have x = 12 and y = 6 . We know they work for 3x – 30 = y  but not if they work for 7y – 6 = 3x . Let's substitute those in to see if (12, 6) really is the solution point.

7y – 6 = 3x  — original equation

7(6) – 6 ≟ 3(12)  — substitute 6 for y and 12 for x

42 – 6 ≟ 36  — simplify by multiplying

36 = 36 ✔  — simplify by combining like terms on left side

Success! It works! We have found our solution!

I hope this helps increase your understanding of the concept. Have a great day!

the terms of a geometric sequence can be found by beginning with the first term and multiplying by the common ratio repeatedly. a recursive formula for a geometric sequence with common ratio r is given by an=ran−1 a n = r a n − 1 for n≥2 n ≥ 2 .

step-by-step explanation: