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# Systems of equations

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I have a few questions I need help with.

What are the steps to solving a system of equation by elimination?

What are the steps to solving a system of equation by substitution?

What are the steps to solving a system of equation by graphing?

Once you have graph a system of equation, how do you check your answer?

When we solve a system of linear equation we get a solution.  It is important to understand what the solution tells us about the system.  Keep that in mind, in your own words what is a inconsistent system?

When we solve a system of linear equation we get a solution.  It is important to understand what the solution tells us about the system.  Keep that in mind, in your own words what is an undetermined system?

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This provides explanations of solving and graphing systems of equations.

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Question -

What are the steps to solving a system of equation by elimination?

There are usually Five steps to solve a system of equation by elimination:-

1. Firstly modify both the given equations in the standard form, Ax + By = C.
2. Determine which variable to eliminate with Addition or Subtraction.
3. Solve for the variable that is left after doing the addition or subtraction operation.
4. Go back and use the found variable in step 3 to find second variable.
5. Check the solution in both equations of the system.

Ex-:
Solve the following system using addition.

2x + y = 9
3x - y = 16

Note that, if I add down, the y's will cancel out. So I'll draw an "equals" bar under the system, and add down:

2x + y = 9
3x - y = 16
5x = 25

Now I can divide through to solve for x = 5, and then back-solve, using either of the original equations, to find the value of y. The first equation has smaller numbers, so I'll back-solve in that one:

2(5) + y = 9
10 + y = 9
y = -1

Then the solution is (x, y) = (5, -1)

Question -

What are the steps to solving a system of equation by substitution?

For Substitution we need to follow these steps:-

1. Choose any variable x or y.
2. Then try to convert one of the equations in such a way that you get ...

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