Systems of Two Linear Equations in Two Variables Practice

Sample questions

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1. Sample 1difficulty 2/5

   Solve the system: $x + y = 10$ and $x - y = 4$. What is the value of $x$?

   • A

     7

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   • B

     5

   • C

     3

   • D

     8

   Why

   Adding the two equations: $2x = 14$, so $x = 7$.

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2. Sample 2difficulty 2/5

   Solve the system: $2x + y = 11$ and $x - y = 1$. What is the value of $y$?

   • A

     3

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   • B

     4

   • C

     1

   • D

     5

   Why

   Adding: $3x = 12$, so $x = 4$. Then $y = x - 1 = 3$.

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3. Sample 3difficulty 2/5

   Two distinct lines in a plane intersect in at most how many points?

   • A

     Infinitely many

   • B

     0

   • C

     2

   • D

     1

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   Why

   Two distinct lines either intersect at exactly one point or are parallel.

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4. Sample 4difficulty 2/5

   Solve: $x + y = 8$ and $2x - y = 1$. What is $x$?

   • A

     4

   • B

     5

   • C

     2

   • D

     3

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   Why

   Adding: $3x = 9$, $x = 3$.

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5. Sample 5difficulty 2/5

   If $y = 2x - 3$ and $y = 5$, what is $x$?

   • A

     2

   • B

     4

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   • C

     3

   • D

     5

   Why

   $5 = 2x - 3$ → $x = 4$.

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