SAT Math: More Systems of Equations Problems

If you’ve read my recent post on Solving Systems of Equations “Cleverly” and you’re looking to try a few more of these problems, you’ll find five more below.  Remember, although you can solve these problems the same way you did in Algebra 1, our goal is to do them in an efficient way so that we can conserve some time that can then be used to solve other problems in the section.

1)  Given the equations 3x + 8y = 24 and 2x – 13y = 26, what is the value of x – y?

(A) 8
(B) 10
(C) 12
(D) 14
(E)  16

2)  Given the equations 10x + 12y = 42 and 6x + 8y = 26, what is the value of x + y?

(A) 4
(B) 5
(C) 6
(D) 7
(E)  8

3)  Mrs. Smith bought three adult tickets and five student tickets for the upcoming holiday concert and spent a total of $44.  Mr. Jones bought five adult tickets and seven student tickets for a total of $68.  If you purchase one adult ticket and one student ticket, how much will you pay, in dollars, for the tickets?

(A)  8
(B)  10
(C)  12
(D)  14
(E)  16

4)  Charlie wants to know how much each of his dogs weighs, but his scale is broken and doesn’t register any weight under 30 pounds.  He begins weighing the dogs in pairs.  Rocco and Boomer weigh a total of 50 pounds.  Rocco and Trixie weigh a total of 40 pounds and Boomer and Trixie weigh a total of 36 pounds.  What is the weight, in pounds, of Boomer?

(A)  13
(B)  21
(C)  23
(D)  25
(E)  28

5)  In the system of equations below, what is the value of x?

3x + 5y – 4z = 10
4x – 2y + 7z12
2x – 3y – 3z = 14

(A)  1
(B)  2
(C)  3
(D)  4
(E)  5

If you have questions about our Systems of Equations strategy, these problems or anything else to do with the SAT, leave a comment or send me an email at info@cardinalec.com .

Answers:

1)  (B)
2)  (A)
3)  (C)
4)  (C)
5)  (D)

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