Intro Systems of Equation

What is the solution to a system of equations?

• It's the ordered pair where both equations equal zero

• It's the ordered pair where graphs of both equations cross the y-axis

• It's the ordered pair (x, y) that makes both equations true.

• It's the ordered pair where graphs of both equations cross the x-axis

What is the solution to the system?

• (0, 3)

• (1, -1)

• (-3, 1)

• (1, 3)

A system has ____________ when two lines intersect at one point. 

• One solution

• No solution

• Infinitely Many Solution

If a system has one solution that means the equations in the system have:

• Same slopes, same y-intercepts

• Same slope, different y-intercepts

• different slopes

Match the following

• point of intersection

• solution of a system of linear equations

• the lines are the same

• one solution

• lines that have different slopes

• System of linear equations

• lines that have the same slope but different y intercepts

• infinitely many solutions

• a set of two or more linear equations in the same variable

• parallel lines

Sstem of linear equations by matrix or Desmos. ​ ​ (a)  

• (5,2)

• (7,0)

• (-10,12)

• (-3,-5)

A system has ____________ when the two equations coincide.

• One solution

• No solution

• Infinitely Many Solutions

Coinciding lines have the...

• Same slopes, same y-intercepts

• Different slopes

• Same slope, different y-intercepts

How many solutions will this system have?

• No Solution

• Infinitely Many Solutions

• No Clue

• One solution

In the system of equations below. What does y equal and therefore can be substituted into the second equation for y?

y = -6
-3x - 6y = 24

• y = -6

• y = 6

• y = -3

• y = 24