Step-by-step explanation:
This one is simple substitution... at least, substitution is the easiest method. The first equation is 3x β 30 = y Β and the second is 7y β 6 = 3x
As I look, I see 3 ways to use substitution to solve this:
substitute 7y β 6 for 3xsubstitute 3x β 30 for ysolve 3x β 30 = y for 3x and make it equal to 7y β 6
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 β 30 = y
7y β 6 = 3x Β β initial system of equations
7y β 6 β 30 = y Β β substitute 7y β 6 for 3x
7y β 6 β 30 = y Β β marking like terms, bold for constants, underlined for variables
7y β 36 = y Β β 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 β6 . For the sake of time, I'm subtracting 7y, though I don't like dealing with negatives.
7y β 7y β 36 = y β 7y Β β subtract 7y from both sides
β36 = β6y Β β simplify
β36 Γ· β6 = β6y Γ· β6 Β β divide by β6 on both sides
y = 6 Β β simplify
Again, we can diverge here: substitute y into 3x β 30 = y or substitute y into 7y β 6 = 3x
I'm going to choose 3x β 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 β 30 = y Β β initial equation
3x β 30 = 6 Β β substitute 6 for y
3x β 30 + 30 = 6 + 30 Β β add 30 to both sides to isolate 3x
3x = 36 Β β simplify the expression
3x Γ· 3 = 36 Γ· 3 Β β divide both sides by 3 to isolate x
x = 12 Β β simplify
So, we have x = 12 and y = 6 . We know they work for 3x β 30 = y Β but not if they work for 7y β 6 = 3x . Let's substitute those in to see if (12, 6) really is the solution point.
7y β 6 = 3x Β β original equation
7(6) β 6 β 3(12) Β β substitute 6 for y and 12 for x
42 β 6 β 36 Β β simplify by multiplying
36 = 36 β Β β 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!