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:

We first multiply the second equation by 4.

So our resulting equation is:

Then we subtract the first equation from the second new equation.

Left Hand Side:

Right Hand Side:

Resulting Equation:

We divide both sides by -15

Left Hand Side:

Right Hand Side:

Our result is:

Let s equal the cost of the shirt and p equal to the cost of a pair of pants. The question can be set up as follows:

The top equation can be multiplied by 4 to give:

The bottom equation can be subtracted from the top equation to give:

Dividing by 5 gives the cost of a pair of pants:

This can be plugged into either one of the initial equations to solve for the cost of the shirt.

Subtracting both sides by 96 gives:

The question asks for the cost of a pair of pants and a shirt which is the sume of the costs. 

Solve for  or  first.  Let's solve for .  To do this, we must eliminate the  variables.  Multiply the first equation by the coefficient of the  variable in the second equation.

Subtract the second equation from the first equation and solve for .

Resubstitute this value to either original equations.  Let's substitute this value into .

Find the common denominator and solve for the unknown variable.

The correct answer is:  

If  then adding  is equal to . If  then  or .  This means that  is equal to  or .