Equations in Two Variables

A solution to a system

of two linear equations

in two variables

must make BOTH

equations TRUE.

• False

• True

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

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

A solution to a

system of linear equations

with two variables

is written as an ordered pair

( x, y ).

• True

• False

?

Mathematical Equivalence

OFF

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

What is pair of linear equations in two variables?

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

• a polynomial with three terms

• set of two linear equations in same two variables

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

• intersecting lines

• parallel lines

• skew lines

• intersecting lines

If a system of linear equations has one solution, what does this mean about the two lines?

• Parallel lines

• the same line

• Intersecting lines