Linear Equations with Two Variables

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

If a system of equations has no solution, what does the graph look like?

• intersecting lines

• parallel lines

• skew lines

• intersecting lines

How can you tell if a point is a solution to a system?

• It makes the first equation true.

• The (x,y) coordinates satisfy both equations

• It makes logical sense

• It makes neither equation negative

The value of c for which the pair of equations cx – y = 2 and 6x – 2y = 3 will have infinitely many solutions is 

• 3 

• – 3 

• –12 

• no value

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

The ordered pair that satisfies (makes them true) all equations in the system is a called a ________________.

• system of equations

• function

• graph

• solution of a system

^{What is the solution?} 

• 1

• -2

• (1, 2)

• (1, -1)