Systems of Equations Quiz

Grade 8 · Math · Quiz

Test your understanding of solving systems of linear equations.

Questions

1. What does the solution to a system of equations represent graphically?

   1. The slope of each line
   2. The y-intercept of each line
   3. The point where the two lines intersect
   4. The x-intercept of each line
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   Answer: The point where the two lines intersect

   The solution (x, y) is the coordinate where both lines meet on a graph.

2. Solve by substitution: y = 2x and x + y = 9. What is x?

   1. 3
   2. 4
   3. 6
   4. 2
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   Answer: 3

   Substitute y = 2x into x + y = 9: x + 2x = 9, so 3x = 9, x = 3.

3. Which system has no solution?

   1. y = 3x + 1 and y = 3x + 5
   2. y = 2x + 1 and y = -x + 4
   3. y = x and y = 2x
   4. y = 4 and x = 2
   Show answer

   Answer: y = 3x + 1 and y = 3x + 5

   Both lines have slope 3 but different y-intercepts, making them parallel with no intersection.

4. If two lines have the same equation, how many solutions does the system have?

   1. 0
   2. 1
   3. 2
   4. Infinitely many
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   Answer: Infinitely many

   If two equations describe the same line, every point on that line is a solution.

5. Solve: x + y = 10 and x - y = 2. What is y?

   1. 4
   2. 6
   3. 8
   4. 2
   Show answer

   Answer: 4

   Add the equations: 2x = 12, x = 6. Substitute: 6 + y = 10, y = 4.

6. What is the first step in the substitution method?

   1. Add both equations together
   2. Solve one equation for one variable
   3. Graph both equations
   4. Multiply both equations by the same number
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   Answer: Solve one equation for one variable

   You isolate a variable in one equation before substituting into the other.

7. The system y = -2x + 3 and y = -2x - 1 has infinitely many solutions.

   Show answer

   Answer: False

   The lines have the same slope (-2) but different y-intercepts (3 and -1), so they are parallel with no solution.

8. In the elimination method, you add or subtract equations to _____ one variable.

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   Answer: eliminate

   The goal of elimination is to cancel (eliminate) one variable so you can solve for the other.

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