To solve this problem, we translate the given information into two equations and then solve both simultaneously. If we let F represent the number of tanks that hold four fish and S represent the number of tanks that hold six fish, the problem tells us that F+S=15. The problem also tells us that 4F (the total number of fish in the 4-fish tanks) plus 6S (the total number of fish in the six-fish tanks) equals 70 (the total number of fish in the aquarium).

Thus we have the following system of equations:

F+S=15

4F+6S=70

Multiplying the first equation by -4 and combing it with the second gives 2S = 10, as seen below:

[-4F-4S=-60 (the first equation times -4)]

2S = 10

Therefore, S, the number of tanks that hold 6 fish, is 5.

Let  be the distance from home to church

Let  be the distance from church to mosque

To solve for y, first eliminate x by adding the two equations together such that the x’s factor out:

4x + 9y + 7 = 0

(–2)2x – (–2) 3y + (–2) 6 = (–2)0 (Multiply this equation by a factor of –2 so that 4x – 4x = 0)

Therefore, the two equations added together are:

(4x + 9y + 7 = 0) + (–4x –(–6)y +(–12) = 0) = (0 + 15y – 5 = 0)

y = 1/3

Let  be the number of dimes Julie has and  be the numbers of quarters she has. The number of dimes and the number of quarters add up to  coins. The value of all quarters and dimes is . We can then write the following system of equations:

To use substitution to solve the problem, begin by rearranging the first equation so that  is by itself on one side of the equals sign:

Then, we can replace  in the second equation with :

Distribute the :

Subtract  from each side of the equation:

Divide each side of the equation by :

Now, we can insert our value for  into the first equation and solve for :

Julie has  quarters and  dimes.

For the second equation, solve for  in terms of .

Plug this value of y into the first equation.

The answer is 7. 

Write two independent equations that represent the problem. 

x + y = 17 and 12x + 7y = 169

If we solve the first equation for x, we get x = 17 – y and we can plug this into the second equation. 

12(17 – y) + 7y = 169

204 – 12y + 7y =169

–5y = –35

y = 7

You can solve this problem in a number of ways, but one way to solve it is by using substitution. You can begin to do that by solving for  in the first equation:

Now, you can substitute in that value of  into the second equation and solve for :

Let's consider this equation as adding a negative 3 rather than subtracting a 3 to make distributing easier:

Distribute the negative 3:

We can now combine like variables and solve for :

We add the two systems of equations:

For the Left Hand Side:

For the Right Hand Side:

So our resulting equation is:

Divide both sides by 10:

For the Left Hand Side:

For the Right Hand Side:

Our result is:

Reduce the second system by dividing by 3.

Second Equation:

     We this by 3.

Then we subtract the first equation from our new equation.

First Equation:

First Equation - Second Equation:

Left Hand Side:

Right Hand Side:

Our result is:

We first add both systems of equations.

Left Hand Side:

Right Hand Side:

Our resulting equation is:

We divide both sides by 3.

Left Hand Side:

Right Hand Side:

Our resulting equation is: