System of Linear Equations (Introduction)

System of Linear Equations (Introduction)

System of Equations

• Two (or more) equations with the same variables

• Example: y=2x+7 and y= -4x-2

• Note that both equations have the same variables (x and y)

Solution to a System of Equations

• Graphically: where the two lines intersect

• There are 3 types of solutions as seen in the picture to the right!

Multiple Choice

How many solutions does this system have?

• One

• None

• Infinite

Multiple Choice

How many solutions does this system have?

• One

• None

• Infinite

Multiple Choice

How many solutions does this system have?

• One

• None

• Infinite

Multiple Choice

How many solutions does this system have?

• One

• None

• Infinite

ONE Solution (x, y)

• The point where the two lines intersect (the solution) satisfies BOTH equations if we substitute the point back into each equation.

• See an example to the right.

Multiple Choice

What is the solution to this system?

• (2, 0)

• (2, -5)

• Infinite Solutions

• No Solution

Multiple Choice

What is the solution to this system?

• (0, 2)

• No Solution

• (-1, 2)

• (-2, -2)

• Infinite Solutions

Multiple Choice

What is the solution to this system?

• (1, -2)

• No Solutions

• Infinite Solutions

• (0, -3)

Multiple Choice

What is the solution to this system?

• (-3, -4)

• No Solution

• Infinite Solutions

• (0, -4)

• (-2, -3)

Thanks for playing!