Question

selesaikan sistem persamaan linear dua variabel berikut dengan menggunakan metode subtitusi 5x+3y= 16 dan x+3y=8

Answer 1

The solution set for the system of linear equations $5x + 3y = 16$ and $x + 3y = 8$is$\boxed{\left\{ {\left( {{\mathbf{2,2}}} \right)} \right\}}$.

Further explanation:

It is given that the system of linear equations are $5x + 3y = 16$and$x + 3y = 8$.

Consider the given equations as follows:

$\begin{aligned}5x+3y=16\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,......\left(1\right)\hfill\\x+3y=8\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,......\left(2\right)\hfill\\\end{aligned}$

Isolate the variable $y$ in terms of $x$ from equation (1) as follows:

$\begin{aligned}5x+3y&=16\\3y&=16-5x\\y&=\frac{{16-5x}}{3}\\\end{aligned}$

Therefore, the value of $y$ in terms of $x$ is$\frac{{16-5x}}{3}$.

Now, substitute $\frac{{16-5x}}{3}$ for $y$ in the equation (2) as follows:

$x+3\left({\frac{{16-5x}}{3}}\right)=8$

The variable is eliminated in the above equation.

Simplify the equation as follows:

$\begin{aligned}x+3\left({\frac{{16-5x}}{3}}\right)&=8\\x+16-5x&=8\\-4x+16&=8\\-4x&=8-16\\\end{aligned}$

Further simplify theequation.

$\begin{aligned}-4x&=-8\\x&=\frac{8}{4}\\x&=2\\\end{aligned}$

Therefore, the value of $x$is ${\mathbf{2}}$.

Substitute $2$ for $x$ in the equation (1) and obtain the value of $y$ as shown below.

$\begin{aligned}5\left(2\right)+3y&=16\\10+3y&=16\\3y&=16-10\\3y&=6\\\end{aligned}$

Further simplify the above equation.

$\begin{aligned}y&=\frac{6}{3}\\&=2\\\end{aligned}$

Therefore, the value of $y$is ${\mathbf{2}}$.

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

Check whether the obtained solution $\left( {2,2} \right)$ satisfies the given equations or not.

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

$\begin{aligned}5\left(2\right)+3\left(2\right)\mathop&=\limits^?16\hfill\\\,\,\,\,\,\,\,\,\,\,\,\,10+6\mathop&=\limits^?16\hfill\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,16&=16\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left( {{\text{True}}}\right)\hfill\\\end{aligned}$

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

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

$\begin{aligned}2+3\left(2\right)\mathop&=\limits^?8\hfill\\\,\,\,\,\,\,\,2+6\mathop&=\limits^? 8\hfill\\\,\,\,\,\,\,\,\,\,\,\,\,\,\,8&=8\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\left({{\text{True}}}\right)\hfill\\\end{aligned}$

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

Thus, the solution set for the system of linear equations $5x + 3y = 16$ and $x + 3y = 8$is$\boxed{\left\{ {\left( {{\mathbf{2,2}}} \right)} \right\}}$.

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,$5x + 3y = 16$,$x + 3y = 8$

Answer 2

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