Solving Systems With Elimination

  • CCSS.Math.Content.HSA-REI.C.5
  • CCSS.Math.Content.HSA-REI.C.6
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1) Solve the system.
5x + 2y = 6
7x + 2y = 14

Explanation

The given system of equations is 5x + 2y = 6 and 7x + 2y = 14. By solving the system, we can find the values of x and y that satisfy both equations. However, the given answer (4,-7),(4, -7) is incorrect. The correct answer should be (4,-7) as it is the only solution that satisfies both equations.

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About This Quiz
Solving Systems With Elimination - Quiz

This quiz focuses on solving systems of equations using the elimination method. It assesses the ability to manipulate and solve linear equations, enhancing algebraic skills crucial for academic advancement in mathematics.

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2) Solve the system.
x + 2y = 2
-x + 3y = 13

Explanation

The given answer (-4,3), (-4,3) is the solution to the system of equations x + 2y = 2 and -x + 3y = 13. When substituting x = -4 and y = 3 into both equations, we get the following: -4 + 2(3) = 2 which simplifies to -4 + 6 = 2, and -(-4) + 3(3) = 13 which simplifies to 4 + 9 = 13. Therefore, both equations are satisfied by the values x = -4 and y = 3, confirming that (-4,3), (-4,3) is the correct answer.

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3) Solve the system.
9x - 3y = 39
-9x + 7y = -79

Explanation

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4) Solve the system.
-3x + 10y = -41
3x - 5y = 16

Explanation

The given answer (-3,-5),(-3, -5) is incorrect. The correct answer should be (-3, -5) because it satisfies both equations in the system. Substituting -3 for x and -5 for y in the first equation, we get -3(-3) + 10(-5) = 9 - 50 = -41, which is equal to the right-hand side of the equation. Similarly, substituting -3 for x and -5 for y in the second equation, we get 3(-3) - 5(-5) = -9 + 25 = 16, which is equal to the right-hand side of the equation. Therefore, (-3, -5) is the correct solution to the system.

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5) Solve the system.
3x - 4y = -16
x - 4y = -40

Explanation

The given system of equations is 3x - 4y = -16 and x - 4y = -40. To solve this system, we can use the method of substitution. From the second equation, we can solve for x in terms of y: x = -40 + 4y. Substituting this value of x into the first equation, we get 3(-40 + 4y) - 4y = -16. Simplifying this equation, we get -120 + 12y - 4y = -16. Combining like terms, we get 8y = 104. Dividing both sides by 8, we get y = 13. Substituting this value of y into the second equation, we get x - 4(13) = -40. Simplifying this equation, we get x - 52 = -40. Adding 52 to both sides, we get x = 12. Therefore, the solution to the system is (12,13).

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Solve the system.5x + 2y = 67x + 2y = 14
Solve the system.x + 2y = 2-x + 3y = 13
Solve the system.9x - 3y = 39-9x + 7y = -79
Solve the system.-3x + 10y = -413x - 5y = 16
Solve the system.3x - 4y = -16x - 4y = -40
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