Lesson 8 Homework Practice Solve System Of Equations Algebraically

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How to Solve System of Equations Algebraically: Lesson 8 Homework Practice

If you are looking for a way to practice solving system of equations algebraically, you have come to the right place. In this article, we will show you how to use the substitution and elimination methods to find the solution of a system of two linear equations. We will also provide you with some examples and exercises that you can use for your lesson 8 homework practice.

What is a System of Equations?

A system of equations is a set of two or more equations that have the same variables. For example, the following is a system of two equations with two variables x and y:

x + y = 5

2x - y = 1

The solution of a system of equations is the ordered pair (x, y) that makes both equations true. For example, the solution of the system above is (2, 3) because when we plug in x = 2 and y = 3 into both equations, we get:

2 + 3 = 5

2(2) - 3 = 1

There are different methods to solve a system of equations algebraically, such as substitution and elimination. We will explain how these methods work in the next sections.

How to Solve System of Equations by Substitution?

The substitution method is a way to solve a system of equations by isolating one variable in one equation and then plugging it into the other equation. This way, we can reduce the system to one equation with one variable that we can solve easily. Here are the steps to follow:

Pick one equation and solve for one variable in terms of the other.

Substitute the expression you found in step 1 into the other equation.

Solve for the remaining variable.

Plug in the value you found in step 3 into either equation to find the other variable.

Check your solution by plugging it into both equations.

Let's see an example:

Solve the system of equations by substitution:

x + y = 5

2x - y = 1

Solution:

We can pick either equation and solve for either variable. Let's pick the first equation and solve for x in terms of y:

x + y = 5

x = 5 - y

We can substitute x = 5 - y into the second equation:

2x - y = 1

2(5 - y) - y = 1

10 - 2y - y = 1

10 - 3y = 1

-3y = -9

y = 3

We have found the value of y. Now we can plug it into either equation to find x. Let's use the first equation:

x + y = 5

x + 3 = 5

x = 2

We have found the solution: (x, y) = (2, 3).

We can check our solution by plugging it into both equations:

x + y = 5

2 + 3 = 5

5 = 5

2x - y = 1

2(2) - 3 = 1

4 - 3 = 1

1 = 1

The solution is correct.

How to Solve System of Equations by Elimination?

The elimination method is a way to solve a system of equations by adding or subtracting the equations to eliminate one variable. This way, we can reduce the system to one equation with one variable that we can solve easily. Here are the steps to follow:

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

Add or subtract the equations to eliminate one variable.

Solve for the remaining variable.

Plug in the value you found in step 3 into either equation to find the other variable.

Check your solution by pl 66dfd1ed39

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