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كويز تفاعلي: حل أنظمة المعادلات الخطية بالحذف
أوراق عمل شاملة تتضمن تدريبات متنوعة على حل أنظمة المعادلات الخطية باستخدام طريقة الحذف. تهدف هذه الأسئلة إلى تعزيز مهارات الطالب في التلاعب بالمعادلات جبرياً لإيجاد قيم المتغيرات بدقة. يغطي الاختبار حالات مختلفة تتطلب ضرب المعادلات في ثوابت لتوحيد المعاملات قبل إجراء الحذف.
يرجى الانتباه إلى أن المعلم قام بإعداد الأسئلة فقط، ولم يقم بإعداد الإجابات أو الشروحات المرفقة. وقد تم توليد الإجابات باستخدام تقنيات الذكاء الاصطناعي، لذلك قد تتضمن بعض الأخطاء أو عدم الدقة.
للحصول على الإجابات الصحيحة والمضمونة، يُرجى الرجوع إلى المعلم أو المصدر الدراسي المعتمد.
Question 1
Points: 1
Use elimination to solve the system of equations: 10x + 5y = 30 5x - 3y = -7
Explanation
Multiply the second equation by 2 to get 10x - 6y = -14. Subtracting this from the first equation gives 11y = 44, so y = 4. Substituting y = 4 into the first equation gives x = 1.
Question 2
Points: 1
Use elimination to solve the system of equations: x + y = 2 -3x + 4y = 15
Explanation
Multiply the first equation by 3 to get 3x + 3y = 6. Adding this to the second equation gives 7y = 21, so y = 3. Substituting y = 3 into the first equation gives x = -1.
Question 3
Points: 1
Use elimination to solve the system of equations: x - y = -8 7x + 5y = 16
Explanation
Multiply the first equation by 5 to get 5x - 5y = -40. Adding this to the second equation gives 12x = -24, so x = -2. Substituting x = -2 into the first equation gives y = 6.
Question 4
Points: 1
Use elimination to solve the system of equations: x + 5y = 17 -4x + 3y = 24
Explanation
Multiply the first equation by 4 to get 4x + 20y = 68. Adding this to the second equation gives 23y = 92, so y = 4. Substituting y = 4 into the first equation gives x = -3.
Question 5
Points: 1
Use elimination to solve the system of equations: 6x + y = -39 3x + 2y = -15
Explanation
Multiply the second equation by -2 to get -6x - 4y = 30. Adding this to the first equation gives -3y = -9, so y = 3. Substituting y = 3 into the second equation gives x = -7.
Question 6
Points: 1
Use elimination to solve the system of equations: 2x + 5y = 11 4x + 3y = 1
Explanation
Multiply the first equation by -2 to get -4x - 10y = -22. Adding this to the second equation gives -7y = -21, so y = 3. Substituting y = 3 into the first equation gives x = -2.
Question 7
Points: 1
Use elimination to solve the system of equations: 3x + 4y = -22 -2x + 3y = -8
Explanation
Multiply the first by 2 and the second by 3 to get 6x+8y=-44 and -6x+9y=-24. Adding them gives 17y=-68, so y=-4. Substituting gives x=-2.
Question 8
Points: 1
Use elimination to solve the system of equations: 3x + 4y = 29 6x + 5y = 43
Explanation
Multiply the first equation by -2 to get -6x - 8y = -58. Adding this to the second equation gives -3y = -15, so y = 5. Substituting y = 5 into the first equation gives x = 3.
Question 9
Points: 1
Use elimination to solve the system of equations: 8x + 3y = 4 -7x + 5y = -34
Explanation
Multiply the first by 5 and the second by -3 to align the y coefficients. Adding the resulting equations gives 61x = 122, so x = 2. Substituting x = 2 gives y = -4.
Question 10
Points: 1
Use elimination to solve the system of equations: 8x + 3y = -7 7x + 2y = -3
Explanation
Multiply the first by 2 and the second by -3 to eliminate y. Adding gives -5x = -5, so x = 1. Substituting x = 1 into the second equation results in y = -5.
Question 11
Points: 1
Use elimination to solve the system of equations: 4x + 7y = -80 3x + 5y = -58
Explanation
Multiply the first by 3 and the second by -4 to eliminate x. Adding gives y = -8. Substituting y = -8 into the second equation results in x = -6.
Question 12
Points: 1
Use elimination to solve the system of equations: 12x - 3y = -3 6x + y = 1
Explanation
Multiply the second equation by 3 to get 18x + 3y = 3. Adding this to the first equation gives 30x = 0, so x = 0. Substituting x = 0 into the second equation gives y = 1.
Question 13
Points: 1
Use elimination to solve the system of equations: -4x + 2y = 0 10x + 3y = 8
Explanation
From the first equation, 2y = 4x or y = 2x. Substituting into the second gives 10x + 3(2x) = 8, which means 16x = 8, so x = 0.5. Then y = 2(0.5) = 1.
Question 14
Points: 1
Use elimination to solve the system of equations: 3x - 3y = -6 -5x + 6y = 12
Explanation
Multiply the first equation by 2 to get 6x - 6y = -12. Adding this to the second equation gives x = 0. Substituting x = 0 into the first equation gives -3y = -6, so y = 2.
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