Linear Equations in Two Variables

A solution to a

system of linear equations

with two variables

is written as an ordered pair

( x, y ).

• True

• False

A solution to a system

of two linear equations

in two variables

must make BOTH

equations TRUE.

• False

• True

If the lines given by 3x + 2ky = 2 and 2x + 5y + 1 = 0 are parallel, then the value of k is 

• –5/4

• 2/ 5 

• 15/4

• 3/2

The equations 4x + 3y = 5 and 12x + 9y = 15 represent 

• No  solution

• Infinite many solution

• Unique solution

Alexandra finds that she can give 3 haircuts and 2 hair dyes in 315 minutes. Giving 2 haircuts and 4 hair dyes takes 450 minutes.  Which system of equations represents the situation?

• 3x + 2y = 315
  2x + 4y = 450

• 3x + 2y = 450
  2x + 4y = 315

• 2x + 2y = 315
  3x + 4y = 450

What is the solution to a system of equations?

• The point that the equations have in common.

• The point where the two lines intersect.

• All of the above.

For what values of a and b does the following pair of equations have an infinite numbers of solutions. 2x+3y=7, a(x+y)-b(x-y)=3a+b-2

• a = 5, b = - 1

• a = - 5, b = 5

• a = 5, b = 1

• a = 1, b = 5

For what value of k will the following equations have infinitely many solutions? 2x-3y=7, (k+1) x+ (1-2k) y=5k-4

• 1

• 2

• 3

• 5

For what value of k will pair of equations have no solution? 3x+y=1 , (2k-1)x+(k-1)y=2k+1

• 1

• 2

• 3

• 4

There are 50 donkeys and chickens on a farm. There are a total of 174 legs. Which system below can be used to figure out how many of each animal the farm has?

• d + c = 174

  4d + 2c = 50

• d + c = 50

  4d + 2c = 174

• d + c = 50

  2d + 4c = 174

• d + c = 174

  2d + 4c = 50