Solving Systems of Linear Equations by Graphing
What is the point of intersection?
Two lines intersect on a graph, representing the solution to a system of linear equations.
What is to isolate the variable?
This is the goal when solving for a variable in one of the equations when using substitution.
What is multiplication?
To use elimination, the equations often need to be adjusted by doing this operation to both sides.
What is inconsistent?
This is the term for a system of equations that has no solution.
What is slope-intercept form? (y=mx + b)
This is the form you want your equations in to easily identify the slope and y-intercept for graphing.
What is substitute?
The substitution method, You solve for one variable and then do this with the expression into the other equation.
What is no solution?
If elimination results in something like 0=5, the system has this type of solution.
What is consistent?
A system with at least one solution is called this.
What are parallel lines?
When graphing, this is the term for two lines that never intersect and have the same slope.
What is y?
If you solve for y in the equation y= x + 2, then you can substitute x + 2 in for this variable in the other equation.
What is (x,y)?
This is the ordered pair that represents the solution to a system of linear equations.
What is independent?
This is the term for a system of equations that has exactly one solution.
What is a graph?
A representation used to find the solution to a system of linear equations.
What is a variable?
a variable is a symbol (often just a single letter like “x”) that stands in for an unknown numerical value in an equation.
What is standard form?
Before you can eliminate, you need to make sure the equations are in this form.
What is slope?
Lines that are parallel have the same of this.
What are infinitely many solutions?
When graphing two linear equations, if you end up with two lines that are exactly on top of each other, the system has this many solutions.
What are infinitely many solutions?
When using substitution, if you end up with a statement like 5=5, the system has this many solutions.
What are coefficients?
This is what you call the numbers in front of the variables.
What is one solution?
If two lines have different slopes, they have this many solutions.