Introduction to Systems of Equations
The process of finding the point where two lines intersect on a graph.
What is solving a system of equations?
The first step in using substitution to solve a system of equations.
What is solve one equation for one variable?
The goal of elimination is to do this to one of the variables.
What is eliminate, or remove, the variable?
The first step in solving a word problem with systems of equations.
What is define the variables?
Solving systems of equations can be applied to this real-world activity involving cost comparisons.
What is budgeting?
The total number of solutions possible when solving systems of equations graphically.
What are zero, one, or infinitely many?
After substituting the expression into the second equation, this is the next step.
What is solve for the remaining variable?
The first step in the elimination method.
What is add or subtract the equations to eliminate one of the variables?
Converting a word problem into these helps identify the systems of equations.
In business, using systems of equations can help determine this about a product.
What is the break-even point?
The two main methods used to solve systems of equations.
What are substitution and elimination?
The type of system where substitution is typically most efficient.
What is a system where one equation is already solved for one variable?
If the coefficients of a variable are not suitable for elimination, this should be done.
What is multiply one or both equations by a number to obtain opposite coefficients?
Number of equations needed to solve a word problem with two variables.
What are two equations?
This field of science heavily uses systems of equations to predict outcomes?
What is physics?
A system of equations with exactly one solution represents this kind of lines on a graph.
What are intersecting lines?
The final step after finding the value of one variable using substitution.
What is substitute the value back into the first equation to find the other variable?
Outcome when elimination results in a false statement like 3=5.
What is no solution?
A word problem that involves age relationships over several years can often be solved effectively using this method.
What is the elimination method?
Systems of equations are used in map making to calculate this between points?
What are distances?
A system of equations with no solution is represented by these types of lines.
What are parallel lines?
When a substitution results in an identity such as 0 = 0, this describes the system
What is an infinitely many solutions system (dependent)?
After eliminating one variable and finding the value of the other, the next step is this.
What is substitute back to find the eliminated variable?
What is the substitution method?
When planning a project, systems of equations can be used to allocate these efficiently.
What are resources?