7x+21y-7=x+3y-1 GCF 7
your statement of 7x+21y-7=x+3y-1 GCF 7
is a false statement.
write it as
7x + 21y - 7
= 7(x + 3y - 1)
To find the greatest common factor (GCF) of 7 in the equation 7x + 21y - 7 = x + 3y - 1, we need to simplify the equation first.
Step 1: Combine like terms on both sides of the equation.
(7x - x) + (21y - 3y) - 7 = -1
Simplifying further, we get:
6x + 18y - 7 = -1
Step 2: Move the constant term to the other side.
6x + 18y = -1 + 7
6x + 18y = 6
Step 3: Divide each term by the GCF, which is 6.
(6x/6) + (18y/6) = 6/6
x + 3y = 1
Now the equation is simplified and we can see that the GCF of 7 has been divided out.
To solve the equation 7x + 21y - 7 = x + 3y - 1, we first want to simplify the equation by combining like terms.
Let's start by rearranging the equation so that all the x terms are on one side and all the y terms are on the other side:
7x - x + 21y - 3y = -1 + 7
Simplifying this further, we have:
6x + 18y = 6
Next, we can factor out the greatest common factor (GCF) if it exists. In this case, the GCF is 6, as both 6x and 18y are divisible by 6.
Dividing both sides of the equation by the GCF, we get:
6(x + 3y) = 6
Now, divide both sides of the equation by 6 to isolate the expression (x + 3y):
x + 3y = 1
So, the simplified form of the equation 7x + 21y - 7 = x + 3y - 1 is x + 3y = 1.