Lesson 8 Homework Practice Solve Systems Of Equations Algebraically Page 51
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Lesson 8 Homework Practice Solve Systems Of Equations Algebraically Page 51
Lesson 8 Homework Practice: How to Solve Systems of Equations Algebraically (Page 51)
A system of equations is a set of two or more equations that have the same variables. To solve a system of equations algebraically, you can use different methods such as substitution, elimination, or graphing. In this article, we will explain how to use the substitution and elimination methods to solve systems of equations algebraically. We will also show you some examples from Lesson 8 Homework Practice on page 51 of your textbook.
Substitution Method
The substitution method is a way of solving a system of equations by replacing one variable with an expression that contains the other variable. This way, you can reduce the system to one equation with one variable, which you can then solve. Here are the steps to follow:
Pick one of the equations and solve for one variable in terms of the other.
Substitute the expression you found in step 1 into the other equation. This will give you an equation with one variable.
Solve the equation from step 2 for the remaining variable.
Plug the value you found in step 3 into the expression from step 1 to find the value of the other variable.
Check your solution by plugging both values into the original equations and verifying that they are true.
Here is an example from page 51 of your textbook:
To solve this system using the substitution method, we can follow these steps:
We can pick the first equation and solve for y in terms of x: y = 3x - 5
We can substitute y = 3x - 5 into the second equation: x + (3x - 5) = 11
We can solve for x by simplifying and isolating x: 4x - 5 = 11 => 4x = 16 => x = 4
We can plug x = 4 into y = 3x - 5 to find y: y = 3(4) - 5 => y = 7
We can check our solution by plugging x = 4 and y = 7 into the original equations:
4 + 7 = 11 (true)
4 + (3 * 4) - 5 = 11 (true)
Therefore, our solution is (x, y) = (4, 7).
Elimination Method
The elimination method is another way of solving a system of equations by eliminating one variable from both equations. This way, you can also reduce the system to one equation with one variable, which you can then solve. Here are the steps to follow:
Align the equations so that the like terms are in columns.
Add or subtract the equations to eliminate one variable. You may need to multiply one or both equations by a constant first to make the coefficients of one variable equal or opposite.
Solve the resulting equation for the remaining variable.
Plug the value you found in step 3 into either original equation to find the value of the eliminated variable.
Check your solution by plugging both values into the original equations and verifying that they are true.
Here is another example from page 51 of your textbook:
To solve this system using the elimination method, we can follow these steps:
We can align the equations so that the like terms are in columns:
x + y = 11
x + 3y -5 =11
We can subtract the second equation from the first equation to eliminate x: 9160f4acd4
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