Linear Systems Module

Line A is represented by the equation given below:

x + y = 2

What is most likely the equation for line B, so that the set of equations has infinitely many solutions?

• 2x + 2y = 2

• 2x + 2y = 4

• 2x + y = 2

• x + y = 4

Two lines, A and B, are represented by the equations given below:

Line A: y = x − 6

Line B: y = 3x + 4

Which of the following shows the solution to the system of equations and explains why?

• (−5, −11), because the point satisfies both equations

• (−5, −11), because the point does not lie on any axis

• (−3, −5), because the point satisfies one of the equations

• (−3, −5), because the point lies between the two axes

The graph shows two lines, A and B.

Based on the graph, which statement is correct about the solution to the system of equations for lines A and B?

• (3, 4) is the solution to line A but not to line B.

• (0, 2) is the solution to both lines A and B.

• (3, 4) is the solution to both lines A and B.

• (0, 2) is the solution to line A but not to line B.

Four equations are graphed on the coordinate grid:

Which set of equations has (−2, 5) as its solution?

• A and B

• B and D

• B and C

• A and D

Would (5, -2) be a solution for this system of equations?

• Yes

• No

Which graph best represents the solution to the following pair of equations?

y = 4x + 2

y = x + 5

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A set of equations is given below:

Equation E: a = 5b + 1 Equation F: a = 3b + 4

Which statement describes a step that can be used to find the solution to the set of equations?

• Equation F can be written as

  b + 1 = 3b + 4.

• Equation F can be written as

  a = 3(a − 1) + 4.

• Equation F can be written as

  a = 5(a − 4) + 1.

• Equation F can be written as

  5b + 1 = 3b + 4.

A set of equations is given below:

Equation C: y = 3x + 7

Equation D: y = 3x + 2

How many solutions are there to the given set of equations?

• One solution

• Two solutions

• Infinitely many solutions

• No solution

Two equations are given below:

m + 3n = 10

m = n − 2

What is the solution to the set of equations in the form (m, n)?

• (1, 3)

• (2, 4)

• (0, 2)

• (4, 6)

A system of equations is shown below:

y = 3x − 7

y = 2x + 1

What is the solution to the system of equations?

• (−8, 17)

• (−8, −17)

• (8, 17)

• (8, −17)