Linear System Properties

A solution of the system 2x+y=7 and 5x-y=14 is (3, 1). How are the graphs of the two equations related?

• The graphs are parallel.

• The graphs coincide.

Translate the phrase into a mathematical statement:

"The difference between twice a number x and number y is 12"

Note: Do not put spaces in typing your answer.

Complete the statement below:

A dependent system is _______________________.

• a system with no solution

• a system dependent on a variable

• a system that is independent

• a system where graph coincides

Complete the statement below: An independent linear system is _______________________

• a system with equations that are identical

• a system with exactly one solution

• a system of lines

• a system with equations that are satisfied by every real number

This system has _____ solutions.

• 0

• 1

• 2

• Infinitely many

Does the system have one, none or infinite solutions?
8x + 4y = 12
y = -2x + 3

• (0,3)

• (3,0)

• No solution(parallel lines)

• Infinitely many solutions

How many solutions?

• One Solution

• No solution

• Infinitely Many Solutions

What is the solution to this system of equations?

• (4, -1)

• (-1, 4)

• (-4, 1)

• (-4, -1)

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

• (1, 5)

• (5, 1)

• (0.25, 2)

• ∅

Solve for x and y
y = 2x + 1
y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)