Big Ideas Math Blue Book Chapter 5 - Systems of Linear Equations

Two or more equations with the same variables is called?

A system of equations

The solution to a system of linear equations

An ordered pair (x, y) that makes every equation in the system true.

same

Coinciding lines have the same slope and the ________ y-intercept.

The method of eliminating one variable by adding or subtracting (combining) two equations with a common term is called the _____________ method.

Elimination

infinitely

Given a system of two linear equations, if the lines are coinciding (over-lapping), there are ___________ many solutions.

no

Given a system of two linear equations, if the lines are parallel, there is ____ solution.

one

Given a system of two linear equations, if the lines have different slopes, there is ____ solution.

You can solve a system of linear equations using the graphical method by finding the point of ______________ .

Intersection (the ordered pair where the lines cross)

When a system of equations has no solution, what do the graphed lines look like?

Lines are Parallel with different y-intercepts

The system has no solution

Parallel lines have no intersection, so there are no solutions

different

Parallel lines have the same slope but _____________ y-intercepts.

infinitely many solutions

Same slope and intercepts, intersects at infinitely many points

A linear equation in the form Ax + By = C is called the ___________ form of a linear equation.

Standard

The______________ method involves expressing one variable in terms of the other variable and substituting an expression into the other equation.

Substitution

A system of equations may be solved algebraically using...

The elimination method or the substitution method

List the three types of SOLUTIONS to a linear system of equations that you have studied. Describe the graph of each type.

The graph of a system with one solution is two intersecting lines. The graph of system with no solutions is two parallel lines. The graph of a system with infinite many solutions is a single line.

The graph has one solution

The point where the lines intersect

When a system of equations has an infinite number of solutions,what do the graphed lines look like?

They are one on top of the other. They are the same line.

A system of linear equations can have a(n) ________ solution, no solution, or infinitely many solutions.

one

A system of linear equations may have _________, ___________, or ____________.

one solution (intersecting lines), no solution (parallel lines), or infinite many solutions (the lines formed are on top of one another).

A system of linear equations consists of linear equations with more than one ____________ .

variable