Answer:
y is equal to -1
x is equal to 4
Step-by-step explanation:
The first thing you would do is multiply the bottom equation by a negative 3. You will get - 6x - 9y = -15. Keep the top equation the same. Both of the 6x's cancel. You then get -11y = 11 so y is equal to negative 1.
Since you have Y, you can now plug that in to any equation to find the value of x. -6x - 2(-1) = 26. You're left with 4. Plug both of the values into each equation to double check.
I hope this picture can explain what is going on in this question
Until the concerns I raised in the comments are resolved, you can still set up the differential equation that gives the amount of salt within the tank over time. Call it
.
Then the ODE representing the change in the amount of salt over time is
and this with the initial condition
You have
Integrating both sides gives
Since
, you get
so the amount of salt at any given time in the tank is
The tank will never overflow, since the same amount of solution flows into the tank as it does out of the tank, so with the given conditions it's not possible to answer the question.
However, you can make some observations about end behavior. As
, the exponential term vanishes and the amount of salt in the tank will oscillate between a maximum of about 100.4 lbs and a minimum of 99.6 lbs.
Tsk Tsk
<span>Write a justification for Line 2,
Line 3, and Line 4. Explain why you chose each justification.</span>
<span><span>Line
1 5x – 2 = 3x + 7</span>
<span>Line 2
2x – 2 = 7 </span>
<span>Line 3
2x = 9 </span>
<span>Line 4 x = 4.5</span></span>
Answer:
Line 2:
subtraction property (subtract 3x from each side)
Line 3: addition property. (add 2 to each side)
<span>Line 4: division property (divide 2 from each side)</span>
Answer:
30 hours.
Step-by-step explanation:
Richard can build 15 snowballs in 1 hour
But 2 snowballs melt every 15 minutes
In 1 hour, the number of snowballs that will have melted is:
× 2 = 8
The number of snowballs that will have remained = 15 - 8 = 7
So 7 snowballs will have remained in 1 hour
For 210 snowballs to have remained, it will take:
× 1 = 30 hours.