Solutions to Two Variable Equations

Solve the system:
x + 6y = 17
x - 3y = 8

• (5, 2)

• (11, 1)

• (1, 11)

• no solution

Solve by elimination:
7x+y=-9

-3x-y=5

• No solution

• (1,8)

• (-2,-3)

• (-1,-2)

What would be the first step in finding the solution with elimination?

• cross out the 3y and -3y

• cross out the 4x and x

• change all the signs of the second equation

• add 1 and -11

________________ is a set of two or more equations that have the same variables.

• solution of a system

• elimination method

• system of equations

• table

What is the slope and the y intercept of the following?
y = 3x - 9

• Slope = 3
  y-int = 9

• slope = 3
  y-int = -9

• slope = -9
  y-int = 3

• slope = 9
  y-int = -3

A system of two intersecting lines will have how many solutions?

• One Solution

• Two Solutions

• No Solution

• Infinite Solutions

A system of two identical (overlapping) lines will have how many solutions?

• One Solution

• Two Solutions

• No Solution

• Infinite Solutions

What is the next step in solving this system by elimination?
2x + 3y = 9
5x + 3y = 21

• Nothing - it is ready to go.

• Multiply one equation by -1

• Multiply the top equation by 3.

• Multiply the bottom equation by 7.

A system of two parallel lines will have how many solutions?

• One Solution

• Two Solutions

• No Solution

• Infinite Solutions

What is the number of solutions to the system of equations? (Notice there are two lines graphed one on top of the other.)

• No Solution

• Infinitely Many Solutions

• One Solution

• Two Solutions