Solving Systems Using Substitution.
Flashcard
•
Mathematics
•
8th Grade
•
Practice Problem
•
Hard
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15 questions
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1.
FLASHCARD QUESTION
Front
What is the substitution method in solving systems of equations?
Back
The substitution method involves solving one of the equations for one variable and then substituting that expression into the other equation to find the values of both variables.
2.
FLASHCARD QUESTION
Front
How do you isolate a variable in an equation?
Back
To isolate a variable, you perform algebraic operations (addition, subtraction, multiplication, division) to get the variable on one side of the equation and all other terms on the opposite side.
3.
FLASHCARD QUESTION
Front
What is the first step in solving a system of equations using substitution?
Back
The first step is to solve one of the equations for one variable in terms of the other variable.
4.
FLASHCARD QUESTION
Front
When using substitution, what do you do after substituting the expression into the other equation?
Back
After substituting, you solve the resulting equation for the remaining variable.
5.
FLASHCARD QUESTION
Front
What does it mean for a system of equations to have a unique solution?
Back
A unique solution means that the two equations intersect at exactly one point, resulting in one set of values for the variables.
6.
FLASHCARD QUESTION
Front
What is an example of a system of equations that has no solution?
Back
An example is the system: y = 2x + 1 and y = 2x - 3. These lines are parallel and do not intersect.
7.
FLASHCARD QUESTION
Front
What is an example of a system of equations that has infinitely many solutions?
Back
An example is the system: 2x + 4y = 8 and x + 2y = 4. The second equation is a multiple of the first, meaning they represent the same line.
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