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Algebra 1 Notes SOL A.4 (7.4) Solving Systems by Elimination II Mrs. Griever Name: Block: Date: Linear Systems by Elimination Multiplying First We have looked at solving linear systems by elimination

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How to fill out linear systems by elimination

How to fill out linear systems by elimination:

Begin by writing down the given linear system of equations. For example, if the system is:

2x + 3y = 7

4x - 2y = 1

Choose one of the variables, either x or y, to eliminate first. It is usually easier to start with the variable that has a coefficient of 1 or -1. In the given system, let's eliminate the variable x in the second equation. Multiply the first equation by 2, and the second equation by -2 to make the coefficients of x in both equations equal.

4x + 6y = 14

8x + 4y = -2

01

Now, subtract the second equation from the first equation to eliminate the variable x. In this case, subtract the second equation from the first equation and write down the new equation.

(4x + 6y) - (-8x + 4y) = 14 - (-2)

12x + 2y = 16

Write down this new equation along with the other equation in the system. Now, the system becomes:

12x + 2y = 16

4x - 2y = 1

At this point, the variable x has been eliminated. Now, choose another variable to eliminate. In this case, let's eliminate the variable y. Multiply the second equation by 3 to make the coefficients of y in both equations equal.

12x + 2y = 16

12x - 6y = 3

Subtract the second equation from the first equation to eliminate the variable y. Write down the new equation.

(12x + 2y) - (12x - 6y) = 16 - 3

8y = 13

Solve the new equation obtained from the elimination step for the remaining variable. In this case, solve for y.

8y = 13

y = 13/8

Substitute the value of y into one of the original equations to solve for the other variable. Let's substitute y = 13/8 into the first equation:

2x + 3(13/8) = 7

2x + 39/8 = 7

Solve this equation for x:

2x = 7 - 39/8

2x = 56/8 - 39/8

2x = 17/8

x = 17/16

Who needs linear systems by elimination?

01

Students studying algebra or linear equations in school or university courses may need to learn and use linear systems by elimination.

02

Engineers, mathematicians, and scientists may need linear systems by elimination as a mathematical tool for solving real-world problems, analyzing data, and making predictions.

03

Individuals working in fields such as economics, physics, or computer science might come across linear systems that can be solved using the elimination method, and thus need to know how to use it effectively.

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What is linear systems by elimination?

Linear systems by elimination is a method used in algebra to solve systems of linear equations by manipulating equations to eliminate variables.

Who is required to file linear systems by elimination?

Anyone studying algebra or mathematics may be required to learn and use linear systems by elimination.

How to fill out linear systems by elimination?

To fill out linear systems by elimination, you need to first write down the equations, then eliminate variables by adding or subtracting the equations.

What is the purpose of linear systems by elimination?

The purpose of linear systems by elimination is to find the solution to a system of linear equations, often used in solving real-life problems involving multiple variables.

What information must be reported on linear systems by elimination?

The variables, coefficients, and constants in the equations must be reported when using linear systems by elimination.

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