contestada

of equations:
Twice a number plus three times a second number is negative one. The first number plus four times the second number is
two.​

Respuesta :

calculista

Answer:

The first number is -2 and the second number is 1

see the procedure

Step-by-step explanation:

The complete question is

Translate to a system equation

Twice a number plus three times a second number is negative one. The first number plus four times the second number is two.

Call the first number m and the second number n

Let

m ----> the first number

n ----> the second number

we know that

[tex]2m+3n=-1[/tex] ----> equation A

[tex]m+4n=2[/tex] ----> [tex]m=2-4n[/tex] ----> equation B

Solve the system by substitution

Substitute equation B in equation A

[tex]2(2-4n)+3n=-1[/tex]

solve for n

[tex]4-8n+3n=-1[/tex]

[tex]5n=4+1[/tex]

[tex]n=1[/tex]

Find the value of m

[tex]m=2-4n[/tex] ----> [tex]m=2-4(1)=-2[/tex]

therefore

The first number is -2 and the second number is 1

ustsr

The first and second number is respectively -2 and 1

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Further explanation

Simultaneous Linear Equations could be solved by using several methods such as :

  • Elimination Method
  • Substitution Method
  • Graph Method

If we have two linear equations with 2 variables x and y , then we need to find the value of x and y that satisfying the two equations simultaneously.

Let us tackle the problem!

[tex]\texttt{ }[/tex]

Let:

The First Number = x

The Second Number = y

[tex]/texttt{ }[/tex]

Twice a number plus three times a second number is negative one.

[tex]2x + 3y = -1[/tex] → Equation 1

[tex]\texttt{ }[/tex]

The first number plus four times the second number is two.​

[tex]x + 4y = 2[/tex] → Equation 2

[tex]\texttt{ }[/tex]

Equation 1 - 2(Equation 2) :

[tex](2x + 3y) - 2(x + 4y) = -1 - 2(2)[/tex]

[tex]2x + 3y - 2x - 8y = -1 - 4[/tex]

[tex]-5y = -5[/tex]

[tex]y = -5 \div -5[/tex]

[tex]y = 1[/tex]

[tex]\texttt{ }[/tex]

[tex]x + 4y = 2[/tex]

[tex]x + 4(1) = 2[/tex]

[tex]x + 4 = 2[/tex]

[tex]x = 2 - 4[/tex]

[tex]x = -2[/tex]

[tex]\texttt{ }[/tex]

Learn more

  • Perimeter of Rectangle : https://brainly.com/question/12826246
  • Elimination Method : https://brainly.com/question/11233927
  • Sum of The Ages : https://brainly.com/question/11240586

Answer details

Grade: High School

Subject: Mathematics

Chapter: Simultaneous Linear Equations

Keywords: Simultaneous , Elimination , Substitution , Method , Linear , Equations

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