Rearranging Linear Equations

Find the gradient and y-intercept of the following equation by rearranging.

Select the simultaneous equation method that the working out in adjacent figure uses.

• The Elimination method

• The Substitution method

Solve this system by substitution.

• (1, -4)

• (1, 4)

• (-4, -7)

• (-7, -4)

Solve using elimination. 
−4x − 4y = 0
4x + 4y = 0 

• (−6, −4) 

• Infinite number of solutions  

• (−6, 10) 

• (6, 4) 

Solve the following system using any method.

y = 2/3x - 2

y = -x + 3

• (0,3)

• (0,-3)

• (3,0)

• (-3,0)

Solve the following system using any method.

3x + 2y = 16

7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

Solve the following system using any method.

y = 2x + 1

y = 4x - 1

• (1,3)

• (-1,-3)

• (-1,3)

• (3,1)

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

Some students want to order shirts with their school logo. One company charges $9.65 per shirt plus a setup fee of $43. Another company charges $8.40 per shirt plus a $58 fee. Which equation represents the number of shirts when both companies charge the same amount?

• y = 9.65 + x
  y = 8.40 + x

• y = 9.65x + 43
  y = 8.40x + 58

• y =9.65x
  y = 8.40x

• y = 9.65x - 43
  y = 8.40x - 58

Solve the following system using any method.

y=-x+4

y=2x+4

• (0,4)

• (2,4)

• (-1,3)

• (4,0)