System of Equations Addition Sample Problems

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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:

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.
Use addition or subtraction to eliminate one of the variables.

Example: Addition

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

Answer (x,y):

Example: 2 Equation preparation with subtraction

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

x - 2y = 21
4x - 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

Answer (x,y):