Solving pairs of linear equations in two variables

When two or more linear equations define a relationship between quantities, they form a ________________________.

• System of Linear Equations

• Consistent Systems

• Inconsistent Systems

• Solution of a System of Linear Inequalities

Solve the systems with any method you choose: Check all that apply:

• x= -5/2

• y=-5/2

• No Solutions

• Infinitely Many Solutions

• x=0

The solutions to a system of equations are:

• Two or more equations with the same variables grouped together

• All ordered pairs (points) that make all equations true.

• one solution, no solution, infinite solutions

• Equations in the same problem.

Systems that produce coincident lines when graphed

• Independent System

• Dependent System

• Inconsistent Systems

• Consistent Systems

• Solution Region

Which system of equations has infinitely many solutions?

• 3y = –5x + 7

  3x = –5y – 7

• 3y = x – 4

  3x – 9y = –12

• 2x + y = 2

  –4x – 2y = 4

• 2y = 3x + 6

  4y = 6x + 12

Solve the system of equations.
 $y=-3x-6$  

 $12x+4y=3$  

•  $\left(3,-24\right)$  

•  $\left(-24,3\right)$  

• No solution

• Infinite solutions

Solve:

y = 2x -11

-3y +6x= -15

• (-1.5,-4)

• (1.5,4)

• No solution (parallel lines)

• Infinitely many solutions

y = 4x - 3

y = -3 + 4x

• No Solutions

• Many Solutions

y = -5 - 2x and -2x - 5 = y

• 1 solution

• infinitely many solutions

• no solution

A linear system can have exactly two solutions.

• True

• False