Solving pairs of linear equations in two variables

How many solutions does this system have?

 $y=3x-5$  
 $y=3x-5$  

• one

• infinitely many

• none

• three

Two equations, such as y = 3x -6 and y =12 + 4x, together are called a(n)__________.

• equations
• system of equations
• problem
• algebraic expression

How many solutions does this systems of equations have?

• 0

• 1

• 2

• Cannot Be Determined

 $x+4y=6$ 

  $y=2x-3$  

How many solutions does this system have?

• one

• two

• infinite number

• no solution

Suri makes $15 per hour and gets a weekly bonus of $25. Juan makes $14 per hour and gets a weekly bonus of $50. Is it possible for Suri and Juan to make the same amount of wages, y, by working the same number of hours, x, in one week?

• Yes because the slopes of the equations are different so the system of equations will have one solution.

• No because the slopes of the equations are the same so the system of equations will have no solution.

• Yes because the slopes of the equations are the same so the system of equations will have no solution.

• No because the slopes of the equations are different so the system of equations will have one solution.

Identify the number of solutions for the system of equations: 2x + 3y = 8 and 4x + 6y = 16.

• Infinite solutions

• No solution

• One solution

• Two solutions

How many solutions does this system have?

y = 2x + 4

y = x + 2

• One solution

• No solution

• Infinite solutions

Does the system of equations have one solution, no solutions, or infinite solutions?

y=4x - 5

y = 2/3x +6

• one solution

• no solutions

• infinite solutions

A system of linear equations with fewer equations than variables always has at least one solution.

• True

• False

If the slopes of the two lines in a linear system of equations are ______________, there will be one solution.

• the same

• different