key fact if you are going to write, graph, solve, and check a system of equation

Question

hiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiiii

Answer 1

Step one:  Read the problem carefully

 

Make sure you read the problem  and understand what the problem asks for. 

 

 

Step two: Define variables

 

Once you know what the problem is asking for, define variables for them.  These are the unknowns that you want to find out and is essential in finding the solution to the problem.   Each unknown should be represented by a different variable.

 

We can use x and y for the variables.

 

 

Step three:  Create the equations

 

After the variable setup, you create the appropriate equations using the variables you defined.  When creating the equations, they should be mathematical interpretations of the problem description.  In other words, you are translating parts of the problem description.  Each equation should be unique and should be consistent.  For example, one equation might represent the total number of coins, whereas another equation would represent the total amount established by the coins.

 

Step four (A):  Solving the equations algebraically

 

Use either the elimination or substitution method to solve the equations to find the variables.  Normally, you would have 2 linear equations, each having the same variables.  For example,

 

x + y = 25                               equation 1         (represents the total number of coins.)

0.10x + 0.25y = 100                equation 2          (represents the total amount in dollars.)

 

Notice that each equation has one x variable and one y variable.  x and y each represent a type of coin.

 

 

Step four (B): Solving the equations graphically

 

You will graph each line on the same coordinate system.  When doing so, you want to solve for y.  This means, get the equations into slope-intercept form.  Once you graphed the equations, look for the point of intersection.  That point of intersection is the solution to the system in the ordered pair (x, y).  This also means that you have solved the problem.

 

 

Step five:  Check the system

 

Substitute the values of the variables that you found into the equations to see if they satisfy each other.

 

 

 

Does this help?