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4vir4ik [10]
3 years ago
14

Solve the system of equations 3y+2z=12 and y-z=9

Mathematics
1 answer:
muminat3 years ago
4 0
Mulitply second equation by 2 and add to first

3y+2z=12
<u>2y-2z=18 +</u>
5y+0z=30

5y=30
divide 5
y=6

sub back
y-z=9
6-z=9
minus 6
-z=3
times -1
z=--3

x=-3
y=6
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How many solutions does this system have?
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Answer:

one solution

Step-by-step explanation:

* Lets start to solve the question

- The 1st equation x - y = -4

- The 2nd equation 3x + y = 8

- We will use the elimination method to solve this system of equation

∵ x - y = -4 ⇒ (1)

∵ 3x + y = 8 ⇒ (2)

- Add the two equation (1) and (2) to eliminate y

∴ x + 3x = -4 + 8

∴ 4x = 4

- Divide both sides by 4

∴ x = 1

- Substitute the value of x in equation (1) or equation (2) to find

  the value of y

- We will use equation (1)

∴ 1 - y = -4

Subtract 1 from both sides

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∴ The solution is (1 , 5)

* The system has one solution

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in a survey, 0.82 of students stated they have homework everyday what is this value written as a fraction
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Translate the following statement to an inequality. A number is at most seven. x &gt; 7 x &lt; 7 x ≥ 7 x ≤ 7
damaskus [11]

The required inequality is: x≤7

Step-by-step explanation:

The words have to be considered and observed properly to write an inequality.

At most means, that the value cannot exceed 7.

So,

Let x be a number

Then

A number is at most 7 will be written as:

x\leq 7

as the value of x cannot exceed 7.

The required inequality is: x≤7

Keywords: Inequality, Variables

Learn more about inequalities at:

  • brainly.com/question/3783529
  • brainly.com/question/3799248

#LearnwithBrainly

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Select the correct answer. What is the area of the triangle in the diagram? A. B. C. D. Reset Next Previous5 Next Using Coordina
Komok [63]

The area of the triangle can be calculated using the distance formula if the coordinates are given.

<h3>What is the triangle?</h3>

The triangle can be defined as a three-sided polygon in geometry, and it consists of three vertices and three edges. The sum of all the angles inside the triangle is 180°.

We have a triangle with coordinates on the coordinate plane.

It is required to find the area of the triangle using the coordinate points.

Here the coordinates are not given, so we are assuming the coordinates are (x1, y1), (x2, y2), (0,0)

From the distance formula:

The distance(b) between (0, 0) and (x1, y1):

\rm b = \sqrt{(x_1-0)^2+(y_1-0)^2} \Rightarrow \sqrt{x_1^2+y_1^2}

The distance between (0, 0) and (x2, y2):

\rm h = \sqrt{(x_2-0)^2+(y_2-0)^2} \Rightarrow \sqrt{x_2^2+y_2^2}

So the area of the triangle:

A = bh/2

\rm A = \dfrac{1}{2}\times  \sqrt{x_1^2+y_1^2} \times  \sqrt{x_2^2+y_2^2}

\rm A = \dfrac{1}{2} \sqrt{(x_1^2+y_1^2) (x_2^2+y_2^2)}

Thus, the area of the triangle can be calculated using the distance formula if the coordinates are given.

Learn more about the triangle here:

brainly.com/question/25813512

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