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Jet001 [13]
3 years ago
9

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

Mathematics
2 answers:
Andreyy893 years ago
7 0

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

Further explanation:

It is given that the system of linear equations are 5x + 3y = 16andx + 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 xis {\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 yis {\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 = 8is\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

mote1985 [20]3 years ago
3 0
3x – 7y=16<span> ... Grafik dari persamaan </span>linear dua variabel<span>berbentuk garis luru
s, seperti yang ... SPLDV dengan </span>metode substitusi<span>, perhatikan contoh </span>berikut<span>. .... Jadi solusi </span>sistem persamaan<span> linier di atas adalah </span>x<span> = 2, y = </span>3<span>, z = 4. .... </span>8<span>. Berapakah nilai 6 − 2 jika </span><span>  merupakan penyelesaian dari ...</span>
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