Simalatenous Equations Flashcards
What is a simultaneous equation?
A simultaneous equation is a set of equations with multiple variables that are solved together.
True or False: Simultaneous equations can only have two equations.
False
What is the purpose of solving simultaneous equations?
To find the values of the variables that satisfy all equations at the same time.
Fill in the blank: In a system of equations, the number of solutions can be _____.
zero, one, or infinitely many
What method can be used to solve simultaneous equations?
Methods include substitution, elimination, and graphing.
If 2x + 3y = 6 and x - y = 4, what is the value of x?
x = 5
Which method involves rearranging one equation to express one variable in terms of the other?
Substitution method
True or False: The elimination method adds or subtracts equations to eliminate one variable.
True
What is the first step in the elimination method?
Align the equations so that like terms are in columns.
If the equations are 3x + 4y = 10 and 6x + 8y = 20, what can you conclude?
The equations are dependent and have infinitely many solutions.
Fill in the blank: When graphing simultaneous equations, the point of intersection represents the _____.
solution
What is the graphical representation of a simultaneous equation?
A line in a coordinate plane.
How many solutions exist if the lines are parallel?
Zero solutions.
What does it mean if two equations in a system yield the same line when graphed?
They are equivalent and have infinitely many solutions.
Which of the following is a characteristic of a consistent system of equations? A) No solutions B) One solution C) Infinitely many solutions
B) One solution
If y = 2x + 1 and y = -x + 4, what is the solution for y?
y = 3 when x = 1
True or False: Simultaneous equations can only involve linear equations.
False
What is the standard form of a linear equation?
Ax + By = C, where A, B, and C are constants.
What does it mean for a system of equations to be inconsistent?
It means there are no solutions.
Fill in the blank: The solution to a system of equations is the point where the ____ intersect.
lines
What is the elimination method also known as?
The addition method.
If x + y = 10 and x - y = 2, what is the value of y?
y = 4
True or False: The substitution method can only be used if one of the equations is already solved for one variable.
True
What is the main advantage of the substitution method?
It can be easier to use when one variable is isolated.
What is the significance of the coefficients in a system of equations?
They determine the slope of the lines when graphed.
