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NAME DATE PERIOD 35 Study Guide and Intervention Solving Systems of Equations in Three Variables Systems in Three Variables Use the methods used for solving systems of linear equations in two variables

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How to fill out solving systems of equations

01

First, write down the system of equations that you need to solve. This may involve multiple unknown variables and multiple equations. For example, if you have the equations:

1.1

2x + 3y = 7

1.2

4x - 5y = 10

02

Next, choose a method to solve the system of equations. There are several techniques available, including substitution, elimination, and graphing. Consider the specific characteristics of the system to determine the most appropriate method.

03

If you decide to use substitution, begin by isolating one variable in one of the equations. For instance, from the given example equations:

3.1

Isolate x in the first equation: 2x = 7 - 3y -> x = (7 - 3y)/2

04

Substitute the isolated variable into the other equation. Using the example equations, substitute x:

4.1

4((7 - 3y)/2) - 5y = 10

05

Simplify and solve the resulting equation. Distribute and combine like terms:

5.1

(28 - 12y) - 5y = 10 -> 28 - 12y - 5y = 10 -> 28 - 17y = 10

06

Continue simplifying the equation to isolate the variable. In this case, subtract 28 from both sides:

6.1

-17y = 10 - 28 -> -17y = -18

Solve for y by dividing both sides by -17:

01

y = -18/-17 -> y = 18/17

1.1

Substitute the determined value of y back into one of the original equations. Going back to the given example equations, substitute y in the first equation:

02

2x + 3(18/17) = 7

Simplify and solve the equation for x:

01

2x + (54/17) = 7 -> 2x = 7 - (54/17)

1.1

Continue simplifying the equation. To combine the fractions, find a common denominator:

02

2x = (119 - 54)/17 -> 2x = 65/17

Solve for x by dividing both sides by 2:

x = (65/17)/2 -> x = 65/34

Who needs solving systems of equations?

01

Students studying mathematics or related fields often encounter solving systems of equations in their coursework.

02

Engineers and scientists frequently use systems of equations to model and solve real-world problems.

03

Economists and financial analysts use systems of equations to analyze market trends and make predictions.

04

Architects and designers may use systems of equations to optimize structural designs or determine material quantities.

05

Any individual working with multiple variables and equations, such as in optimization problems or statistical analysis, may benefit from solving systems of equations.

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What is solving systems of equations?

Solving systems of equations involves finding the values of variables that satisfy multiple equations simultaneously.

Who is required to file solving systems of equations?

Anyone studying algebra or mathematics may be required to solve systems of equations.

How to fill out solving systems of equations?

To fill out solving systems of equations, one must carefully analyze and solve each equation, often using methods such as substitution or elimination.

What is the purpose of solving systems of equations?

The purpose of solving systems of equations is to find the intersection point or points where the equations are satisfied simultaneously.

What information must be reported on solving systems of equations?

The solutions to the equations and the steps taken to arrive at those solutions must be reported on solving systems of equations.

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