Intro Systems of Linear Equations

Why will this system have infinite solutions?

• The equations are both negative.

• The equations are the same.

• They have the same y-intercept but not the same slope.

• They have the same slope but not the same y-intercept.

Indicate the number of solutions shown.

• One Solution

• No Solution

• Infinite Solutions

Indicate the number of solutions shown.

• One Solution

• No Solution

• Infinite Solutions

Indicate the number of solutions shown.

• One Solution

• No Solution

• Infinite Solutions

What is the solution?

• (1, -1)

• (-1, 1)

• (0, -2)

• (0, 1)

What is the solution to the systems of equations shown in the graph?

• 1 Solution x=-1/2

• 1 Solution y=-1/2

• Many Solutions

• No Solution

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

A company opened two new branches. Branch M began with 26 clients and gains 3 more per week. Branch Q began with 18 clients and gains 5 more per week. Write a system of equations to compare the number of clients (c) each branch has after (w) weeks.

• 26c + 3w

  18c + 5w

• c = 3w + 26

  c = 5w + 18

• c = 26c + 3w

  c = 18c + 5w

• w = 26 + 3c

  w = 18 + 5c

At a college bookstore, Carla purchased a math textbook and a novel that cost a total of $54, not including tax. If the price of the math textbook, t, is $8 more than 3 times the price of the novel, n, which system of linear equations could be used to determine the price of each book?

• t + n = 54
  t = 3n + 8

• t + n = 54
  n = 3t + 8

• t + n = 54
  t = 3n - 8

• t + n = 8
  t = 3n + 54

A large pizza at Palanzio’s Pizzeria costs $6.80 plus $0.90 for each topping. The cost of a large cheese pizza at Guido’s Pizza is $7.30 plus $0.65 for each topping. Which system of equations could be used to find the number of toppings when both companies cost the same amount?

• y = 6.80 + .65x
  y=7.30+.90x

• x + y = 6.80
  x + y = 7.30

• y = 6.80+.90x
  y = 7.30 + .65x

• y + .90x = 6.80
  y + .65x = 7.30