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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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Find the indicated real nth root(s) of a. n=3, a=729
marissa [1.9K]

Answer:

9

Step-by-step explanation:

n=3, a=729

For any odd integer, n ; a will have only one real nth root which will be a positive integer.

Similarly, for any integer, n, that is > 1 ; related by the expression ;

p^n = a ; the nth root of a = p

Therefore,

If n = 3 ; a = 729

p^3 = 729

To obtain the value of p ; take the cube of both sides

(p^3)*1/3 = 729^1/3

p = 9

Hence, the real nth root of 729 is +9 when n = 3

6 0
2 years ago
The y coordinate of the vertex of f (x)=-x^2+8x+7 is f(4)
azamat

Hello there.

To answer this question, we need to remember some properties about the vertex of quadratic functions.

Let f(x)=ax^2+bx+c,~a\neq0. Its vertex can be found on the coordinates (x_v,~y_v) such that x_v=-\dfrac{b}{2a} and y_v=-\dfrac{b^2}{4a}+c, in which y_v=f(x_v).

Using the coefficients given by the question, we get that:

x_v=-\dfrac{8}{2\cdot(-1)}\\\\\\ x_v=-\dfrac{8}{-2}\\\\\\ x_v=4

Thus, we have:

y=f(x_v)=f(4)

So the statement is true, because the x coordinate of the vertex of the function is equal to 4.~~\checkmark

7 0
2 years ago
Help
enyata [817]
The answer is a hope this helps 
5 0
3 years ago
Read 2 more answers
Explain how you can use place value to discribe how 0.05 and 0.005
VMariaS [17]
They are the same just one has more zeroes.
6 0
3 years ago
Over what interval is the quadratic function decreasing?
frosja888 [35]

The interval over which the given quadratic equation decreases is:  x ∈ (5, ∞).

<h3>How to find the interval of quadratic functions?</h3>

Usually a quadratic graph function decreases either when moving from left to right or moving downwards.

In the given graph, we can see that the coordinate of the vertex is (5, 4) after which the curve goes in the downward direction.

Thus, for the values of x greater than 5, the function decreases and so we conclude that the interval in which the quadratic equation decreases is: (5, ∞).

Read more about Quadratic functions at: brainly.com/question/18030755

#SPJ1

6 0
2 years ago
Read 2 more answers
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