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Here are some tips for System of Equations Addition, which aligns with New York state standards:

System of Equations: Addition

A system of equations is a set of equations that are linked together. The simplest system of equations is two equations with two unknowns.

One way to solve a system of equations is by addition:

1. Prepare the equations so that there is one variable in each equation that has the same coefficient.
This can be done by multiplying one or both equations by a constant.
2. Use addition or subtraction to eliminate one of the variables.

Solve. Answer in the form (x,y). For example: (-2,3)
 x - y = 6-x + 2y = - 9 Answer (x,y):

Step 1: Prepare the equations
When you add x from the first equation and -x from the second equation, the variable x is eliminated.
So nothing needs to be done to prepare the equations.

Step 2: Add the two equations
 x - y = 6 -x + 2y = - 9 y = - 3

Now solve for x.
 x - y = 6 x - (-3) = 6 x + 3 = 6 x + 3 - 3 = 6 - 3 x = 3

Example: 2 Equation preparation with subtraction

Solve. Answer in the form (x,y). For example: (-2,3)
 x - 2y = 214x - 5y = 54 Answer (x,y):

Step 1: Prepare the equations
Since the coefficients do not match for either variable in the two equations, we will need to use multiplication.
Let's multiply the first equation by 4 to get

4x - 8y = 84
4x - 5y = 54

Step 2: Subtract
 4x - 8y = 84 - (4x - 5y = 54) 4x - 8y = 84 -4x + 5y = -54 -3y = 30 y = -10

Now solve for x.
 x - 2y = 21 x - 2(-10) = 21 x + 20 = 21 x + 20 - 20 = 21 - 20 x = 1