Identify Solutions of Linear Systems

When using any of the 3 methods to solve a system of linear equations the resulting solution is the same no matter which method is used.

• True; using any method will result in the correct solution.

• False; the solution varies because the solution depends on which method is used.

What is the solution to this system?

• (-2, -2)

• (2, -2)

• (-2,2)

• (2, 2)

What is the solution to the system of equations? 
y = 3x - 8
y = 4 - x

• (3,1)

• (1,3)

• (-3,1)

• (3,-1)

Solve the system of equations.
y = 4x+1
3x + 2y = 13

• (1, 5)

• (5, 1)

• (0.25, 2)

• ∅

A SOLUTION to a system of linear equations is....

• the x-value that is a solution to both equations

• the y-value that is a solution to both equations

• an ordered pair that is a solution to both equations

• none of these

How can you tell if a point is a solution to a system?

• It makes the first equation true.

• The (x,y) coordinates satisfy both equations

• It makes logical sense

• It makes neither equation negative

If a system of equations has no solution, what does the graph look like?

• intersecting lines

• parallel lines

• same lines

A system of equations will have no solution when...

• it is comprised of 2 parallel lines

• solving algebraically produces zero as an answer

• an attempt to solve makes all variables cancel, leaving an untrue statement (like 5 = -7)

• an attempt to solve makes all variables cancel, leaving a true statement (like 6 = 6)

An ordered pair in a system that makes all equations true is

• consistent system

• system of linear equations

• solution of a system to linear equations

• independent system

The solution to a system of linear equations is a _____.