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photoshop1234 [79]
3 years ago
6

Solve the system using substitution.

Mathematics
2 answers:
Lapatulllka [165]3 years ago
5 0

The solution set for the system of linear equations x + y = 8 and y = 3x is \boxed{\left\{{\left({{\mathbf{2,6}}}\right)}\right\}}.

Further explanation:

It is given that the system of linear equations are x + y = 8 and y = 3x.

Consider the given equations as follows:

x + y = 8\,\,\,      ......(1)

y = 3x\,\,\,          ......(2)

From equation (2), the value of y in terms of x is3x.

Now, substitute 3x for y in the equation (1) as follows:

x + 3x = 8

The variable is eliminated in the above equation.

Simplify the equation as follows:

\begin{aligned}x + 3x&=8\\4x&=8\\x&=\frac{8}{4}\\x&=2\\\end{aligned}

Therefore, the value of x is 2.

Substitute 2 for x in the equation (2) and obtain the value of y as shown below.

\begin{aligned}y&= 3\left( 2\right)\\&=6\\\end{aligned}

Therefore, the value of y is 6.

Thus, the ordered pair for the given system of linear equation is \left({{\mathbf{2,6}}} \right).

Check whether the obtained solution (2,6) satisfies the given equations or not.

Substitute 2 for x and 6 for y in the equation (1) and check the equation.

\begin{aligned}2 + 6\mathop&_=^? 8\hfill \\\,\,\,\,\,\,\,8 &= 8\,\,\,\hfill\\\end{aligned}             (True)

The ordered pair \left({2,6}\right) satisfies the equation (1).

Substitute 2 for x and 6 for y in the equation (2) and check the equation.

\begin{aligned}6\mathop&_= ^? \:3\left( 2 \right)\hfill\\6&= 6\,\,\,\,\,\,\,\,\,\,\,\,\hfill\\\end{aligned}              (True)

The ordered pair \left({2,6}\right) satisfies the equation (2).

Thus, the solution set for the system of linear equations x + y = 8 and y = 3x is \boxed{\left\{{\left({{\mathbf{2,6}}}\right)}\right\}}.

Learn more:

1. Which classification best describes the following system of equations? brainly.com/question/9045597

2. Which polynomial is prime?brainly.com/question/1441585

3. Write the subtraction fact two ways 10-3? brainly.com/question/6208262

Answer Details:

Grade: Junior High School

Subject: Mathematics

Chapter: Linear equations

Keywords: Substitution, linear equation, system of linear equations in two variables, variables, mathematics,x + y = 8 ,y = 3x , solution set

Alexeev081 [22]3 years ago
4 0

Answer:

Option B that is (2,6) is correct

Explanation:

We have been given with system of equations

X+Y=8 and Y=3X

Here, we will substitute the value of Y=3X in X+Y=8

We will get X+3X=8

Further simplification we will get to 4X=8

Hence, the value of X=2

And now, substituting the value X=2 in Y=3X we will get Y=6.

Therefore, option B is correct.

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Answer:

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Step-by-step explanation:

Find the rate of change for the situation.

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Solution

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The median of books to a box is 9 and The mean of books to a box is 11

The complete question is

Garth is packing boxes with books. The list shows how many boxes are in each of 10 boxes. 6,14,6,18,9,9,12,10,11,15

Which statement is true about the number of boxes packed to a box?

A) The median # of books to a box is 8

B) The median # of books to a box is 9

C) The mean # of books to a box is 11

D) The mean # of books to a box is 12

<h3>What is Mean and Median ?</h3>

Mean is the average of the data given while the median is the middle point of the data.

It is given that

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