15 Questions
What method was used to solve the system of linear equations in the first example?
Substitution
In the second example, why was the elimination method chosen over substitution?
The x terms made it a good candidate for elimination
What is a common indicator that elimination can be used in a linear equation system?
Having variables with opposite signs
Why is it important to check the solution by plugging values back into one of the original equations?
To verify that the solution satisfies both original equations
Why was substitution chosen over elimination in the first example?
It was easier to substitute x in terms of y
What does it mean when solving a system of equations if you arrive at 'nonsense' like 8 = 32?
An error has occurred in your calculations
When solving a system of equations, what is a key step after determining the value of one variable?
Plug this value into one of the original equations
'[...]plug in these values for y and z, and solve for x.' What method are you likely using at this point?
'Substitution'
What method is recommended to solve a system of linear equations if there is an indication to temporarily eliminate a variable?
Elimination
When solving the system of equations, which method involves adding two equations together to eliminate a variable?
Elimination
After eliminating a variable in a system of equations, what should be done next to obtain the value of one of the variables?
Substitute the eliminated variable back in one equation
What is a key advantage of using the elimination method over substitution in solving linear equations systems?
Faster computation
When dealing with linear equations systems, why is it important to check the solution by plugging values back into an original equation?
To verify if the solution satisfies all equations
What does it mean if, during the solving process of a linear equation, you end up with 'nonsense' like 8 = 32?
A computational error occurred
'Now, we know two of the three variables - now we can turn back to the original three equations, plug in these values for y and z, and solve for x.' What method are you most likely using at this point?
'Substitution'
Learn the basics of linear equations in algebra, including what they are and how to identify them. Discover the significance of degree 1 in linear equations and explore examples to deepen your understanding.
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