SBAC PREP FOR WEEK OF MARCH 18TH: NUMBER OF SOLUTIONS

How many solutions are there to this equation? 3(x – 1) = 6x – 3

• no solutions

• one solution

• two solutions

• infinite solutions

Which of these equations has NO solution?

• 3(2x + 7) = 6(x + 4) – 3

• 3(6x – 5) = 36(x – 5) + x

• 8(x – 3) + 14 = 2(4x + 5)

• 13x – 7 = 12(x – 1) + x + 5

How many solutions does the system of equations –8x + y = 11 and 3x + y = 11 have?

• no solutions

• 1 solution

• 2 solutions

• an infinite number of solutions

Suppose the first equation in a system of two linear equations is 3x – 5y = 18. The second equation being which of these will cause the system to have an infinite number of solutions?

• 3x – 5y = 14

• 3x – 5y = 18

• 3x – 7y = 14

• 3x – 7y = 18

Suppose the first equation in a system of two linear equations is 12x + 7y = 25. The second equation being which of these will cause the system to have no solution?

• 12x + 7y = 20

• 12x + 7y = 25

• 12x + 9y = 20

• 12x + 9y = 25

Suppose the first equation in a system of two linear equations is –4x + 13y = –2. The second equation being which of these will cause the system to have one solution?

• –26x + 8y = –6

• –8x + 26y = –4

• –4x + 13y = –8

• –4x + 13y = –2

Which of these equations has an infinite number of solutions?

• 2x + r + 5x – 9 = – 6 + 9x – r + 3

• 10x – 6x – 4 – 1 = –7 – 12 + 2x + 2x

• 7x + 5 + 4 – 9x = r + x – 2 + 4 + 8x

• 5x – 2r – 3 – 9 = r – 12 + 3x + 3r

Why does the equation 9 – 2x – 9 – 16x = –14x – 7 – 4x – 11 have no solutions?

• because if you add 18x to both sides of the equation and simplify, you get –18 = – 18

• because if you add 18x to both sides of the equation and simplify, you get 0 = – 18

• because if you subtract 18x from both sides of the equation and simplify, you get –18 = – 18

• because if you subtract 18x from both sides of the equation and simplify, you get 0 = – 18

Which of these equations has no solutions?

• –10 + 8x – 7x + 10 = x + 6 – x – 6

• 21 – 9 + 4x – 5x = 8x – 7x + 4 + 6

• x – 4 + 1 – 7x = – 8x + 4 + 2x – 7

• 3x + 5 – 10x + 8 = x – 8x – 16 – 3

Which of these systems of equations has an infinite number of solutions?

• -6c + 11d = 20

• -6c + 11d = 20

• -5c + 8d = 22

• -5c + 8d = 22