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Test
Math
Domain
Algebra
Skill
Systems of two linear equations in two variables
Difficulty
Hard
ID: 52cb8ea4
Modded SAT Question Bank by Abdullah Mallik

Equation 1: 7 x minus 5 y, equals 4. Equation 2: 4 x minus 8 y, equals 9.

If the ordered pair x comma y is the solution to the system of equations above, what is the value of 3 x plus 3 y ?

  1. negative 13

  2. negative 5

  3. 5

  4. 13

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Correct Answer: B
Rationale

Choice B is correct. Subtracting the second equation, 4 x minus 8 y, equals 9, from the first equation, 7 x minus 5 y, equals 4, results in open parenthesis, 7 x minus 5 y, close parenthesis, minus, open parenthesis, 4 x minus 8 y, close parenthesis, equals, 4 minus 9, or 7 x minus 5 y, minus 4 x, plus 8 y, equals 5. Combining like terms on the left-hand side of this equation yields 3 x plus 3 y, equals negative 5.

Choice A is incorrect and may result from miscalculating 4 minus 9 as negative 13. Choice C is incorrect and may result from miscalculating 4 minus 9 as 5. Choice D is incorrect and may result from adding 9 to 4 instead of subtracting 9 from 4.

 

Question Difficulty: Hard
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