Solving a System of Linear Equations

4) Solve the system of linear equations.

• (1, -3, -4)

• (-1, 3, -4)

• no solution

• infinitely many solutions

Solve the system of equations.

y = -3x + 11

5x + y = 21

• (1, -5)

• (1, 5)

• (-4, 5)

• (5, -4)

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

The equations of two lines are:
 2x-y=4 and y=-2x+8.
What is the value of x in the solution for this system?

• x=8

• x=3

• x=11

• x=5

Solve:
y=8x+1
y=6x+3

• (1, 9)

• (4, 14)

• (0, 1)

• (2, 4)

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

Nancy went to the grocery story.  On Monday she purchased 4 apples and 6 bananas for a total of $13.  On Wednesday she purchased 3 apples and 7 bananas for a total of $13.50.  Which system of equations represents the situation?

• 4x + 6y = 3
  13.5x - 13y = 6

• x + y = 4
  x - y = 6

• 4x + 6y = 13
  3x + 7y = 13.5

• 4x - 6y = 13
  3x - 7y = 13.5

The talent show committee sold a total of 530 tickets in advance. Student tickets cost $3 each and the adult tickets cost $4 each. If the total receipts were $1740, which system could be used to find how many of each type of ticket were sold?

• S + A = 530
  3S + 4A = 1740

• S + A = 530
  4S + 3A = 1740

• S + A = 1740
  3S + 4A = 530

• S + A = 1740
  4S + 3A = 530

What is the best method do you use?

y = 6x − 11

−2x − 3y = −7

• Graphing

• Substitution because a variable is defined

• Set the equations equal to each other.

What is the best method to use?

2x − 3y = −1

y =x − 1

• Graphing

• Substitution because a variable is defined

• Set the equations equal to each other.