SAT Linear Systems Practice: Questions and Answers

Correct answer

Choice D: 7

Explanation

Add the two equations to eliminate y: 3x = 12, so x = 4. The equation x − y = 1 then gives y = 3. Their sum is 7. Checking gives 2 × 4 + 3 = 11 and 4 − 3 = 1.

Why each choice is right or wrong

1. Choice A

   This is x − y, not x + y.

2. Choice B

   This is y alone; the question asks for the sum x + y.

3. Choice C

   This is x alone; add the corresponding y-value 3 to answer the question.

4. Choice D

   Correct answer

   Correct: x = 4 and y = 3, so their sum is 7.

Correct answer

Choice A: No solutions

Explanation

Divide the first equation by 2 to get x + 2y = 6. The second requires the same left side to equal 7. These requirements contradict each other, so no pair can satisfy both equations.

Why each choice is right or wrong

1. Choice A

   Correct answer

   Correct: the equations require one expression to equal two different constants.

2. Choice B

   The lines have equal slopes but different intercepts, so they do not meet.

3. Choice C

   Two distinct straight lines cannot have exactly two intersections.

4. Choice D

   The coefficients are proportional, but the constants do not have the same ratio.

Correct answer

Choice C: 4

Explanation

To make the variable coefficients proportional, the first equation must have twice the second equation's x-coefficient, so k = 4. Twice the second equation is 4x + 6y = 10, which conflicts with 4x + 6y = 9. Thus k = 4 gives no solutions.

Why each choice is right or wrong

1. Choice A

   With k = 2, subtracting the equations gives 3y = 4, leading to one solution.

2. Choice B

   The x-coefficient ratio 3/2 does not equal the y-coefficient ratio 6/3, so the lines meet once.

3. Choice C

   Correct answer

   Correct: the coefficients match at a factor of 2, but the constants do not.

4. Choice D

   The x-coefficient ratio 6/2 differs from the y-coefficient ratio 6/3, so the lines meet once.