Systems of Equations Set Equal

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

What is the solution to the system?

• (-1, 3)

• (-3, 1)

• (3, -1)

• (-3, -1)

What is the number of solutions to the system of equations? (Notice there are two lines graphed one on top of the other.)

• No Solution

• Infinitely Many Solutions

• One Solution

• Two Solutions

To Find the solution to this system of equations, Juan decided to multiply the entire first equation by -1. What method is Juan employing to find the solution?

• Substitution

• Graphing

• No Solution

• Elimination

What is the first step Terri could take to find the solution to the system of equations using the Elimination Method?

• Multiply by -1 through one equation to flip the signs and create opposite y-values.

• Multiply by -1 through one equation to flip the signs and create opposite x-values.

• Multiply by 1 through one equation to flip the signs and create opposite y-values.

• Isolate a variable and substitute the value in the other equation.

To find the solution to the system of equations Tandy looked for opposites to zero each other out. What variable contains opposite coefficients and which method is Tandy using?

• The x-variables are opposites, and Tandy is using Elimination.

• The x-variables are opposites, and Tandy is using Substitution.

• The y-variables are opposites, and Tandy is using Elimination.

• The y-variables are opposites, and Tandy is using Substitution.

The ordered pair that satisfies all equations in the system.

• system of equations

• function

• graph

• solution of a system

If a system of linear equations has one solution, what does this mean about the two lines?

• Parallel lines

• the same line

• Intersecting lines

AJ was asked to find the solution to this system of equations. x = 7 - 2y 2x + y = 5 Noticing that x was isolated and set equal to 7 - 2y, he decided to replace x in the second equation with its value. What method is AJ using and what equation did he write?

• Elimination; 2(7-2y) + y = 5

• Graphing; 2x = (7-2y) + y = 5

• Substitution; 2(7-2y) + y = 5

• Substitution; x = 7 - 2y + 2x + y = 5

Kayla solved the following system and found the solution to be (10, -9). x = -3y - 17 2x + 3y = -7 What would the graph of this system look like?

• A point on the coordinate plane

• Parallel Lines

• Coincident Lines (lines that graph one on top of the other)

• Lines that intersect at one point