Sergeant 6-2 Solving Systems By Substitution Quiz

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| By Courtney Frank
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Courtney Frank
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Quizzes Created: 45 | Total Attempts: 16,314
| Attempts: 99
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  • 1/5 Questions

    Solve the following system by substitution.x + 14y = 842x - 7y = -7What is the y-coordinate of the solution?

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About This Quiz

This quiz challenges students to solve systems of equations using the substitution method, focusing on finding y-coordinates of solutions.

Sergeant 6-2 Solving Systems By Substitution Quiz - Quiz

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  • 2. 

    Solve the following system by substitution.y = 7 - x2x - y =8What is the y-coordinate of the solution?

    Explanation
    To solve the system by substitution, we can rearrange the second equation to solve for x in terms of y. The equation becomes x = 8 - y. We can then substitute this expression for x into the first equation. The first equation becomes y = 7 - (8 - y)². Simplifying this equation gives us y = 7 - (64 - 16y + y²). Further simplification yields y = 7 - 64 + 16y - y². Combining like terms gives us y² - 15y + 57 = 0. Factoring this quadratic equation gives us (y - 3)(y - 19) = 0. Therefore, the possible values for y are 3 and 19. However, substituting y = 19 back into the second equation gives us a negative value for x, which is not possible. Therefore, the only valid solution is y = 3. Hence, the y-coordinate of the solution is 3.

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  • 3. 

    Use substitution to solve the following system.y = 2x + 62x - y = 2

    • (2, 6)

    • (6, 2)

    • Infinitely many solutions

    • No solution

    Correct Answer
    A. No solution
    Explanation
    The given system of equations is y = 2x + 6 and 2x - y = 2. To find the solution, we can substitute the value of y from the first equation into the second equation. Substituting y = 2x + 6 into 2x - y = 2, we get 2x - (2x + 6) = 2, which simplifies to -6 = 2. Since this equation is not true, there is no solution to the system of equations.

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  • 4. 

    Solve the following system by substitution.3x + y = 12y = -x - 2 

    • (-9, 7)

    • (-7, 9)

    • (7, -9)

    • (7, 9)

    Correct Answer
    A. (7, -9)
    Explanation
    To solve the system of equations by substitution, we can start by solving the second equation for y. From the second equation, we have y = -x - 2. We can substitute this expression for y into the first equation, giving us 3x + (-x - 2) = 12. Simplifying this equation, we get 2x - 2 = 12. Solving for x, we find x = 7. Substituting this value of x back into the second equation, we find y = -9. Therefore, the solution to the system of equations is (7, -9).

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  • 5. 

    Use substitution to solve the following system.x - 2y = 34x - 8y = 12

    • (12, 0)

    • (0, 12)

    • Infinitely many solutions

    • No solution

    Correct Answer
    A. Infinitely many solutions
    Explanation
    The given system of equations can be solved using substitution. By rearranging the first equation, we can express x in terms of y as x = 34 + 2y. Substituting this value of x into the second equation, we get 34 + 2y - 8y = 12. Simplifying this equation, we find -6y = -22, which implies y = 22/6 = 11/3. Substituting this value of y back into the first equation, we find x = 34 + 2(11/3) = 34 + 22/3 = 136/3. Therefore, the solution to the system of equations is (136/3, 11/3), which is not one of the given answer choices. Thus, the correct answer is infinitely many solutions.

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  • Dec 15, 2024
    Quiz Edited by
    ProProfs Editorial Team
  • Nov 12, 2014
    Quiz Created by
    Courtney Frank
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