Solving System Equations

Solve for x and y
2x − 3y = −1
 y = x − 1

• (-2,-3)

• (0,-1)

• (3,4)

• (4,3)

Solve the system given:
-x + y = -4
y = 2x - 11

• (3,7)

• (7,3)

• (4,-3)

• (-3,4)

Solve this system by substitution.

• (1, -4)

• (1, 4)

• (-4, -7)

• (-7, -4)

If a system of equations has infinitely many solutions, what does the graph look like? 

• intersecting lines

• parallel lines

• skew lines

• the same line (coinciding lines)

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

Solve:
8x + 4y = 12
y = -2x + 3

• (0,3)

• (3,0)

• No solution(parallel lines)

• Infinitely many solutions

David is running a concession stand at a soccer game. He sells nachos and sodas. Nachos cost $1.50 each and sodas cost $0.50 each. At the end of the game, David made a total of $78.50 and sold a total of 87 nachos and sodas combined. Which system of equations represents this situation?

• 1.5x+0.5y=78.5
  x+y=87

• 1.5x+0.5y=78.5
  1.5x+0.5y=87

• x+y=78.5
  1.5x+0.5y=87

• x+y=78.5
  x+y=87

Solve for x and y
5x + 3y = 7
y = 4

• (4,1)

• (4,-1)

• (1,4)

• (-1,4)

How many solutions will this system have? 

• No solution

• One Solution

• I Don't Know

• Infinitely Many Solutions

The first step in solving using the substitution method is __________.

• get x by itself

• get y by itself

• get either variable by itself

• add the equations together