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# Lesson 8 Homework Practice Solve Systems Of Equations Algebraically

## Lesson 8 Homework Practice Solve Systems Of Equations Algebraically

A system of equations is a set of two or more equations that relate two or more variables. Solving a system of equations means finding the values of the variables that make all the equations true at the same time. There are different methods to solve systems of equations, such as graphing, substitution, and elimination. In this lesson, we will focus on the elimination method, also known as the linear combination method.

## What is the elimination method?

The elimination method is a way of solving systems of equations by adding or subtracting the equations to eliminate one of the variables. The goal is to create a simpler system of equations that has only one variable. Then, we can solve for that variable and use its value to find the other variable(s).

For example, consider the system of equations:

3x + 2y = 8 x - y = -2

We can eliminate the variable y by adding the two equations. This gives us:

4x + y = 6

Now we have a simpler equation with only one variable, x. We can solve for x by dividing both sides by 4:

x = 6/4 x = 3/2

We can use this value of x to find y by substituting it into one of the original equations. For example, using the second equation, we get:

x - y = -2 (3/2) - y = -2 y = (3/2) + 2 y = 7/2

Therefore, the solution of the system is (3/2, 7/2), which means x = 3/2 and y = 7/2.

## How to use the elimination method?

To use the elimination method, we need to follow these steps:

• Choose one of the variables to eliminate.

• If necessary, multiply one or both equations by a constant to make the coefficients of the chosen variable equal or opposite.

• Add or subtract the equations to eliminate the chosen variable.

• Solve for the remaining variable.

• Substitute the value of the remaining variable into one of the original equations to find the value of the eliminated variable.

• Check the solution by plugging it into both original equations.

## Example

Solve the system of equations below by using the elimination method. Write your answer as a coordinate point.

6x - 5y = 21 2x + 5y = -5

Solution:

• We choose to eliminate y because it has the same coefficient in both equations.

• We do not need to multiply any equation because the coefficients of y are already opposite.

We add the two equations to eliminate y. This gives us:

• 8x = 16

We solve for x by dividing both sides by 8:

• x = 16/8 x = 2

We substitute x = 2 into one of the original equations to find y. For example, using the first equation, we get:

• 6x - 5y = 21 6(2) - 5y = 21 12 - 5y = 21 -5y = 9 y = -9/5

• We check the solution by plugging x = 2 and y = -9/5 into both original equations. We see that they are both true, so our solution is correct.

The answer is (2, -9/5), which means x = 2 and y = -9/5.

### References

• [Systems of equations Algebra 1 Math Khan Academy]

• [Lesson 8 Systems of Linear Equations 8th Grade Mathematics Free Lesson Plan]

• [Solving systems of linear equations Lesson - Khan Academy]

## Practice Problems

Now that you have learned how to use the elimination method to solve systems of equations, you can try some practice problems on your own. Here are some examples of systems of equations that you can solve by using the elimination method. Write your answers as coordinate points.

4x + 3y = 12

• 2x - 3y = -6

-3x + 2y = 9

• 6x - 4y = -18

5x - 2y = 7

• -10x + 4y = -14

3x + y = 5

• -9x - 3y = -15

2x + y = 4

• -4x - 2y = -8

To check your answers, you can use the [online calculator] to solve systems of equations by using the elimination method. You can also watch the [video tutorial] to see how to use the elimination method step by step.

### Summary

In this lesson, you learned how to solve systems of equations algebraically by using the elimination method. The elimination method is a way of solving systems of equations by adding or subtracting the equations to eliminate one of the variables. The steps to use the elimination method are:

• Choose one of the variables to eliminate.

• If necessary, multiply one or both equations by a constant to make the coefficients of the chosen variable equal or opposite.

• Add or subtract the equations to eliminate the chosen variable.

• Solve for the remaining variable.

• Substitute the value of the remaining variable into one of the original equations to find the value of the eliminated variable.

• Check the solution by plugging it into both original equations.