System of Linear Equations - Part 1

Two or more equations with the same variables is called?

A system of equations

What method would be easiest to solve this system? 2x + 3y =4 2x -9y =-32

Elimination method: Subtracting 2x and 2x will Eliminate the x value and allow us to solve for "y". Then use "y" to find "x". (BTW: the x = 2.5, y = 3)

infinitely

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

The graph has one solution

One intercept

infinitely many solutions

Same slope and intercepts, intersects at infinitely many points

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

The solution to the system

Any ordered pair that makes every equation in the system true. It is also the interception.

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

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 (same coordinate for both equations)

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

Parallel and different y-intercept

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.

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

What method would be easiest to solve this system? 4x + 2y = 14 3x + y = 10

Substitution: subtract 3x from both sides to make the equation: y= -3x +10. Substitute this into 4x + 2y = 14 in place of "y" and solve for x. Then use "x" to find "y" (BTW: x=3, y=1)

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

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

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.

TRUE

Two lines, each with a different slope, can have the same y-intercept. TRUE or FALSE

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

one