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2 years ago

Solve the system of equations. – 9y + 4x – 11 = 0 - 3y + 10x + 31 = 0

Mathematics

1 answer:

Kruka [31]2 years ago

5 0

value of x =-4 and value of y=-3

(-4,-3) is the solution of system of equations.

Step-by-step explanation:

We need to solve the system of equations

$-9y + 4x-11 = 0- 3y + 10x + 31 = 0$

Rearranging:

$-9y + 4x = 11\,\,\,eq(1)\\- 3y + 10x=- 31 = 0\,\,\,eq(2)$

Multiply eq(2) with 3 and subtract eq(2) from eq(1)

$-9y + 4x = 11\\-9y+30x=-93\\+\,\,\,\,\,\,-\,\,\,\,\,\,\,\,\,\,\,\,+\\----------\\-26x=104\\x=\frac{104}{-26}\\x=-4$

Putting value of x = -4 into eq(1)

$-9y + 4x = 11\\-9y+4(-4)=11\\-9y-16=11\\-9y=11+16\\-9y=27\\y=\frac{27}{-9}\\y=-3$

So, value of x =-4 and value of y=-3

(-4,-3) is the solution of system of equations.

Keywords: system of equations.

Learn more about system of equations at:

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A multiple-choice test contains 10 questions. There are four possible answers for each question. a) In how many ways can a stude

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Answer :

<h3> $4^{10}$ <u> =1048576 ways </u> a student can answer the questions on the test if the student answers every question.</h3>

Step-by-step explanation:

Given that a multiple-choice test contains 10 questions and there are 4 possible answers for each question.

∴ Answers=4 options for each question.

<h3>To find how many ways a student can answer the given questions on the test if the student answers every question :</h3>

Solving this by product rule

Product rule :

<u>If one event can occur in m ways and a second event occur in n ways, the number of ways of two events can occur in sequence is then m.n</u>

From the given the event of choosing the answer of each question having 4 options is given by

The 1st event of picking the answer of the 1st question=4 ,

2nd event of picking the answer of the 2nd question=4 ,

3rd event of picking the answer of the 3rd question=4

,....,

10th event of picking the answer of the 10th question=4.

It can be written as by using the product rule

$=4.4.4.4.4.4.4.4.4.4$

$=4^{10}$

$=1048576$

<h3>∴ there are 1048576 ways a student can answer the questions on the test if the student answers every question.</h3>

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<u>Step-by-step explanation:</u>

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