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3 years ago

use the substitution method to solve the system of equations choose the correct orderd pair. 3x-y=7 2x-2y=2

Mathematics

1 answer:

sergey [27]3 years ago

6 0

Answer:

(3,2)

Step-by-step explanation:

We are given the system:

3x-y=7

2x-2y=2.

We are asked to solve this by substitution. We need to pick an equation and pick a variable from that equation to solve for that variable.

I really like either for this. Some people might go with the first one though. Let's do that. I will solve the first one for y.

3x-y=7

Subtract 3x on both sides:

-y=-3x+7

Divide both sides by -1:

y=3x-7

Now we are ready for substitution. We are going to plug this equation into the second equation giving us:

2x-2y=2 with y=3x-7 gives us:

2x-2(3x-7)=2

Distribute:

2x-6x+14=2

Combine like terms:

-4x+14=2

Subtract 14 on both sides:

-4x =2-14

Simplify:

-4x =-12

Divide both sides by -4:

x =-12/-4

Simplify:

x =3

So using y=3x-7 and x=3, I will find y now.

y=3x-7 if x=3

y=3(3)-7 (I inserted 3 for x since we had x=3)

y=9-7 (Simplified)

y=2 (Simplified)

The answer is (x,y)=(3,2).

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a new rectangular park is planned.it will be 3/4 kilometer long and have an area of 3/8 square kilometers. how many kilometers w

kakasveta [241]

<em>The word usage in last sentence of the question is not well presented. However, I can understand that you intend to solve for the width of the park</em>

Answer:

$Width = 2\ km$

Step-by-step explanation:

Given

$Length = \frac{3}{8}km$

$Area = \frac{3}{4}km^2$

Required

Determine the Width

For a rectangle:

$Area = Length * Width$

Substitute for Area and Length

$\frac{3}{4} = \frac{3}{8} * Width$

Multiply both sides by $\frac{8}{3}$

$\frac{8}{3} * \frac{3}{4} = \frac{3}{8} * \frac{8}{3}* Width$

$\frac{8}{3} * \frac{3}{4} = Width$

$\frac{24}{12} = Width$

$2 = Width$

$Width = 2\ km$

6 0

3 years ago

Use Gaussian elimination to write each system in triangular form

Feliz [49]

Answer:

To see the steps to the diagonal form see the step-by-step explanation. The solution to the system is $x = -\frac{1}{9}$ , $y= -\frac{1}{9}$ , $z= \frac{4}{9}$ and $w = \frac{7}{9}$

Step-by-step explanation:

Gauss elimination method consists in reducing the matrix to a upper triangular one by using three different types of row operations (this is why the method is also called row reduction method). The three elementary row operations are:

Swapping two rows
Multiplying a row by a nonzero number
Adding a multiple of one row to another row

To solve the system using the Gauss elimination method we need to write the augmented matrix of the system. For the given system, this matrix is:

$\left[\begin{array}{cccc|c}1 & 1 & 1 & 1 & 1 \\1 & 1 & 0 & -1 & -1 \\-1 & 1 & 1 & 2 & 2 \\1 & 2 & -1 & 1 & 0\end{array}\right]$

For this matrix we need to perform the following row operations:

$R_2 - 1 R_1 \rightarrow R_2$ (multiply 1 row by 1 and subtract it from 2 row)
$R_3 + 1 R_1 \rightarrow R_3$ (multiply 1 row by 1 and add it to 3 row)
$R_4 - 1 R_1 \rightarrow R_4$ (multiply 1 row by 1 and subtract it from 4 row)

$R_2 \leftrightarrow R_3$ (interchange the 2 and 3 rows)

$R_2 / 2 \rightarrow R_2$ (divide the 2 row by 2)
$R_1 - 1 R_2 \rightarrow R_1$ (multiply 2 row by 1 and subtract it from 1 row)
$R_4 - 1 R_2 \rightarrow R_4$ (multiply 2 row by 1 and subtract it from 4 row)
$R_3 \cdot ( -1) \rightarrow R_3$ (multiply the 3 row by -1)
$R_2 - 1 R_3 \rightarrow R_2$ (multiply 3 row by 1 and subtract it from 2 row)
$R_4 + 3 R_3 \rightarrow R_4$ (multiply 3 row by 3 and add it to 4 row)
$R_4 / 4.5 \rightarrow R_4$ (divide the 4 row by 4.5)

After this step, the system has an upper triangular form

The triangular matrix looks like:

$\left[\begin{array}{cccc|c}1 & 0 & 0 & -0.5 & -0.5 \\0 & 1 & 0 & -0.5 & -0.5\\0 & 0 & 1 & 2 & 2 \\0 & 0 & 0 & 1 & \frac{7}{9}\end{array}\right]$

If you later perform the following operations you can find the solution to the system.

$R_1 + 0.5 R_4 \rightarrow R_1$ (multiply 4 row by 0.5 and add it to 1 row)
$R_2 + 0.5 R_4 \rightarrow R_2$ (multiply 4 row by 0.5 and add it to 2 row)
$R_3 - 2 R_4 \rightarrow R_3$ (multiply 4 row by 2 and subtract it from 3 row)

After this operations, the matrix should look like:

$\left[\begin{array}{cccc|c}1 & 0 & 0 & 0 & -\frac{1}{9} \\0 & 1 & 0 & 0 & -\frac{1}{9}\\0 & 0 & 1 & 0 & \frac{4}{9} \\0 & 0 & 0 & 1 & \frac{7}{9}\end{array}\right]$

Thus, the solution is:

$x = -\frac{1}{9}$ , $y= -\frac{1}{9}$ , $z= \frac{4}{9}$ and $w = \frac{7}{9}$

7 0

3 years ago

What is 5/6 times 3/10

hichkok12 [17]

That will be;
5/6 x 3/10
15/60
3/12
1/4
Hope i helped

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3 years ago

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Simora [160]

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plug that into the point slope formula, with either point. generally use the most simple point
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simply if you want

Y = -2x +4 -2 = -2x +2

or

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3 years ago

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vlabodo [156]

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