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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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