Answer: 4 cakes
Explanation: 2/3 is equal to 4/6. Each cake only takes 1/6 lbs. of sugar
Answer:
x=70
Step-by-step explanation:
x/10=7
First you need to get the x by itself, so you should do the opposite of what is happening to the x.
In this case the x is being divided so you would need to multiply.
So multiply the x by 10 and this gets it by itself.
But you have to do to one side what you do to the other.
So multiply the other side by 10 as well!
This equals x=70
To show work on both sides, show the multiplication of both sides by 10
Answer:
{x,y} = {19/12,5/6}
Step-by-step explanation:
By definition, we have

So, we have to solve two different equations, depending of the possible range for the variable. We have to remember about these ranges when we decide to accept or discard the solutions:
Suppose that 
In this case, the absolute value doesn't do anything: the equation is

We are supposing
, so we can accept this solution.
Now, suppose that
. Now the sign of the expression is flipped by the absolute value, and the equation becomes

Again, the solution is coherent with the assumption, so we can accept this value as well.
Answer:
The system is consistent; it has one solution ⇒ D
Step-by-step explanation:
A consistent system of equations has at least one solution
- The consistent independent system has exactly 1 solution
- The consistent dependent system has infinitely many solutions
An inconsistent system has no solution
In the system of equations ax + by = c and dx + ey = f, if
- a = d, b = e, and c = f, then the system is consistent dependent and has infinitely many solutions
- a = d, b = e, and c ≠ f, then the system is inconsistent and has no solution
- a ≠ d, and/or b ≠ e, and/or c ≠ f, then the system is consistent independent and has exactly one solution
In the given system of equations
∵ -2y + 2x = 3 ⇒ (1)
∵ -5y + 5x = 12 ⇒ (2)
→ By comparing equations (1) and (2)
∵ -2 ≠ -5
∵ 2 ≠ 5
∵ 3 ≠ 12
→ By using the 3rd rule above
∴ The system is consistent independent and has exactly one solution
∴ The system is consistent; it has one solution