Linear Equations Labyrinth

Given the following system of equations:

y = 2x + 5

y = -4x + 2

Graph these equations on a coordinate plane. What is the x-coordinate of the solution to this system?

Mathematical Equivalence

ON

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What type of solution does the following system of equations* have?

2x + 3y = 6

4x + 6y = 12

*Both of these are in standard form and need to be converted to y = mx + b

• One solution

• No solution

• Infinitely many solutions

• Two solutions

Solve the following system of equations by graphing:

y = -2x + 5

y = 3x - 1

What is the solution?

• (1, 3)

• (2, 1)

• (1, 2)

• (2, -1)

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Given the following system of equations:

y = 2x + 6

-3x + 4y = 9

What is the solution when these two equations are graphed?

*One equation is in standard form and needs to be converted to y = mx + b

• (2, 2)

• (-3, 0)

• (1, 1)

• (0, 2)

Look at the graph of two lines that never intersect. What type of solution does this system have?

• One solution

• No solution

• Infinitely many solutions

• Exactly two solutions

Two graphs are shown above. What is the systems of equations represented by the graphs?

• y = 2x + 2

  y = x +1

• y = ½x + 2

  y = -x +1

• y = ½x + 2

  y = x +1

• y = 2x + 2

  y = -x +1

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Which of the following systems of equations might be represented by the graph?

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There are 15 plates in a kitchen cabinet. The diameter of each plate is either 7 inches or 12 inches. The diameter of all 15 plates combined is 140 inches.
Which system of equations can be used to find the number of 7-inch plates, x, and the number of 12-inch plates, y, that are in the cabinet?

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The two tables represent the values that correspond to a system of linear equations. What s the solution to this system of linear equations?

• (0, 2)

• (-2, 6)

• (-1, -5)

• (1, 0)

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The graph represents a system of two linear equations in two variables. What is the system of linear equations that is shown on the graph?

• y = -3x + 4 and

  y = 3x – 2

• y = 3x + 4 and

  y = 3x + 2

• y = -3x + 1 and

  y = 3x – 2

• y = 4x – 3 and

  y = -2x + 3

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