Algebra Systems of Equations Solving Graphs

Solve the following system of equations using the process of substitution. If your results involve a special case of linear systems, classify the appropriate response as "infinitely many solutions" or "no real solutions." (Section 3.2)

• (1, 3)

• (-1, -8)

• (1, 2)

• (3, -1)

WITHOUT GRAPHING
what can you say about these lines

• Consistent and Dependent

• Consistent and Independent

• Neither

• Inconsistent

Which of the following options is a solution to the system provided? Confirm by directly plugging in the solutions below to the system (Section 3.1):

• (3, 2)

• (2, 3)

• (4, 1)

• (1, 4)

Solve the following system:
3x + 2y = 16
7x + y = 19

• (-2,5)

• (-2,-5)

• (2,-5)

• (2,5)

Given the equations below, how can we eliminate the terms with x?

x + 2y = 15

2x + y = 19.5

• subtract the two equations from each other

• multiply the second equation by -1 and add the two equations

• multiply first equation by 2, multiply the second equation by 1 then add them

• multiply the first equation by -2 then add the equations together 

Solve the system of equations.
y = 4x+1
3x + 2y = 13

• (1, 5)

• (5, 1)

• (0.25, 2)

• ∅

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 the system of equations.
x + 2y = -3
x - y = -12

• (-9, 3)

• (-7 ,5)

• (3, 15)

• (9, 6)

The graph of f(x) and g(x) are shown below. How many solutions does the system of equations have?

• One

• Two

• Three

• Four

• No Solution

A system of equations that has a least one solution is

• Consistent

• inconsistent

• dependent

• independent