Solve the systems, if possible. a.) a + 2y = 1( mod 5), 2.x + y = 1( mod 5).

Q: Solve the linear congruence 13x = 2(mod27) (a) 23 (b) 16 (c) 12 (d) 6 (e) has no solution

A: See solution below

Q: Given the following system of linear simultaneous congruences what is the value of x that satisfies…

A: According to the given information, it is required to find the value of x that satisfies all…

Q: Find (a) ∣A∣, (b) ∣B∣, (c) AB, and (d) ∣AB∣. Then verify that ∣A∣∣B∣ = ∣AB∣.

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Q: 4. Find solutions of the system of congruences x = 3 (mod 7), x = 1 (mod 5), x = 4 (mod 6). a) 964…

A: I have used chinese remainder theorem

Q: Find solutions to the system of :equivalences 2x = 3 (mod 7) Зx 9 (тоd 15) 5х %3D 20 (тоd 60) 385…

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Q: Find all incongruent solutions to the system of congrucnces. 16x = 8 (mod 3) 2.x = 3 (mod 5) 5.x =…

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Q: ). Hence, solve for the system below 7x + 3y = 10 (mod 16) 2x + 5y = 9 (mod 16)

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Q: Solve the following IBVP: 0 0, u(x,0) = 2 – 2x2, u(x,0) = 0, 0 0, %3D %3!

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Q: 14 is a solution to the system x ≡ 2 (mod 3) x ≡ 4(mod 5) x ≡ 5 (mod 7)   Select one: True…

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Q: B. Verify if the given values of x are solutions to the equations/ ined 1. 7x + 2 = 9 2. 3x-5 4 srps…

A: 1. 7x+2=92. 3x-5=43. x+8<64. -4x≥15. 3x+1≥7

Q: Let k be a real number. By using Cramer's rule, the solution of the following system is: S2x +2y =…

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Q: Solve the following system of linear congruences: 7x + 3y = 10 (mod 16) 2.x + 5y = 9 (mod 16)

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Q: 1. Solve each of the linear congruence equations or verify that it has no solution. (i). 3r = 4(mod…

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Q: Solve for u. 2u-11u+31 (4-7)- If there is more than one solution, separate themn with commas. U =…

A: This problem is related to quadratic equations and we solve this using root formula.

Q: Let k be a real number. By using Cramer's rule, the solution of the following system is: (2x-2y 0…

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Q: Let k be a real number. By using Cramer's rule, the solution of the following system is: (2x – 2y =…

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Q: (3) Solve the system of congruences: I = 2 mod 5 I = 3 mod 8 I = 7 mod 11

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Q: Let k be a real number. By using Cramer's rule, the solution of the following system is: (2x – 2y =…

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Q: Solve the following system of equations using Cramer’s rule [5] { −3? + 2? − 6? = 6 5? + 7? − 5? = 6…

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Q: Find the solution to an = 5an-2 — 4а, 4 with ao 3, aj = 2, a2 =6, and az = 8. Find the solution to…

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Q: The system x E 3 mod 9, x E 2 mod 4, has O A. no solution. O B. Unique solution. O C. finitely many…

A: Introduction: The Chinese remainder theorem is very significant in solving a system of linear…

Q: Given the system of congruencies: x=1 mod 3, x=2 mod 5, x=3 mod 7. Then the solution is ______

A: We will use here chinese remainder theorem. Chinese remainder theorem. Let n1,n2,n3,. . . nr be…

Q: Find solutions to the system of equivalences: 2х3D 3 (тod 7) 3x 3D9 (тod 15) 5x = 20 (mod 60) 386…

A: Given the system of equivalences:

Q: Q.31 If a+b+c=5 and ab+bc+ ca=10, then prove that a +b³ +c³ – 3abc=-25 Q.32 Prove that :

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Q: 52х + 67y + 46z %3D 175 67х + 73у + 54z %3D 194 46х + 54y + 65z %3D 165

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Q: Find all solutions to the system of congruences I =1 (mod 2), 1 = 2 (mod 3), I = 3 (mod 5), and I=4…

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Q: Find all solution to the system of congruences. 2x = 10 (mod 11) х3 3 (тоd 13) х3 1 (тоd 15)

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Q: Find the value of n that will make each of these equations true. 1. n-7=30 2. n-6=8 3. 5n = 25 %3D n…

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Q: need help with this question:   Find all solutions to the system of congruences x ≡ 1 (mod 2), x ≡…

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Q: Let k be a real number. By using Cramer's rule, the solution of the following system is: S2x + 2y =…

A: Equations in matrix form, 2223*Xy=2k0 A*X= B VALUE of A= (3*2-2*2)= 6-4 |A|= 2   In Cramer's rule we…

Q: Let k be a real number. By using Cramer's rule, the solution of the following system is: S 2x – 2y =…

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Q: Which of the following statements is CORRECT? x³ + x 1 = 0 has no solution in [0, 2] Ox³ + x-1=0 has…

A: Given equation is x3+x-1=0 Our question is to determine how many solutions of the given equation in…

Q: 4. Use Cramer's rulc to solve the lincar systemn. r+ 3y 2 5.r +7y 3

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Q: Solve the system of congruence 3x + 7y = 10 (mod 16) ( 5x + 2y = 9( mod 16) . Hint: Eliminate x by…

A: Given system of congruence is  3x+7y≡10(mod16)5x+2y≡9(mod16) we have to solve this.

Q: ind the solutions of the following system: x + 2y = 1 (mod 5) 2x + y = 1 (mod 5) + 3y = 1 (mod 5)

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Q: 1. Given the systems of lir

A: Given,           5x1-2x2+3x3=-1-3x1+9x2+x3=2    2x1-x2-7x3=3

Q: 21 41 Verify the following directly if A = 1. B = |; .c = [, а. A(ВC) %3D (АB)C b. А(B+C) %3 AB + AC…

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Q: Solve the linear congruence 7а + 3у %3D 10 (тod16).

A: Consider the linear congruence 7x + 3y ≡ 10 mod 16.Since gcd (7, 3) = 1 we know at least one…

Q: 19, Obtain the eight incongruent solutions of the linear congruence 3x + 4y = 5 (moi 84 ELEMENTARY…

A: To obtain the eight incongruent solutions of the linear congruence.

Q: 1. Find all solutions to the system of congruence. (Use CRT) x = 1 (mod 2) х3 2 (тоd 3) х%3 3 (тod…

A: Consider system  x≡1mod2,  x≡2mod3, x≡3mod5, x≡4mod11 Here,  a1=1, a2=2, a3=3, a4=4m1=2, m2=3, m3=5,…

Q: and 16. For two attributes A and B, we have (AB)=8; (4) 18, (aB) = 5 and N= 35. Calculat& the…

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Q: (: :)-- (;) (:) -- (") a ven if the complete d 2 lution to this system is r = nere a is any real…

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Q: Let k be a real number. By using Cramer's rule, the solution of the following system is: (3x + 4y =…

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Q: Show that if A is singular and Ax = b, b = 0, has one solution, then it has infinitely many.

A: Given: A is singular and Ax = b, b = 0

Q: The least positive solution modulo 330 for the system x = 2(mod 5) x = 5(mod 6) x = 3(mod 11) is x =…

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Q: 10. Find all solutions of the system of congruencies x = 2 mod 3 x = 4 mod 5 х З тod 7

A: Use Chinese remainder theorem Answer and explanation is given below

Q: Find solutions to the system :of equivalences 2х %D 3 (тоd 7) 3x = 9 (mod 15) 5х 20 (mod 60)

A: Given: To Find: Value of x.

Q: 10. Find solutions of the system of congruences x = 3 (mod 7), x = 1 (mod 5), x = 4 (mod 6). a) 964…

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Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.