Solving Linear Equations Flashcards
What is an equation?
An equivalence between two mathematical expressions.
What are solutions?
The numbers that can be substituted for variables in an equation to make that equation true.
What does it mean to solve an equation?
To find the solution to the equation.
What does it mean to satisfy an equation?
It means to find the numbers to use for the variables that make the equation true.
What are equivalent equations?
Equivalent equations are equations that have the same solution.
What is a linear equation?
A linear equation is an equation whose variables are not multiplied together.
For example, x+2=3 is a linear equation, but x^2+4=3 does not.
What is an ordered pair?
A solution to an equation with two or more variables.
E.g. an ordered pair for an equation in terms of x and y would be in the form (x, y): (2, 3), etc.
What is a system of equations?
A set of equations in two or more variables.
What are simultaneous equations?
The equations in a system of equations.
What is substitution?
Solving one equation in terms of a single variable and plugging the other side of that equation into another equation to solve for one variable.
What is elimination?
Elimination is done when one equation is substracted from another equation to eliminate one or more variables.
Both sides of one or more equation(s) can be multiplied by a constant before subtracting if needed.
How do you solve a linear equation with one variable?
You combine like terms and simplify until you find the solution.
What does it mean for an equation to have no solutions?
If the simplest form of the equation is not true.
e.g. x+3=x+10 equates to 3=10, which is not true.
What is an equation called that is true for all values of x?
An identity
