Question

Of equations:

Answer 1

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

$2m+3n=-1$ ----> equation A

$m+4n=2$ ----> $m=2-4n$ ----> equation B

Solve the system by substitution

Substitute equation B in equation A

$2(2-4n)+3n=-1$

solve for n

$4-8n+3n=-1$

$5n=4+1$

$n=1$

Find the value of m

$m=2-4n$ ----> $m=2-4(1)=-2$

therefore

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

Answer 2

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!

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Let:

The First Number = x

The Second Number = y

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

$2x + 3y = -1$ → Equation 1

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

$x + 4y = 2$ → Equation 2

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Equation 1 - 2(Equation 2) :

$(2x + 3y) - 2(x + 4y) = -1 - 2(2)$

$2x + 3y - 2x - 8y = -1 - 4$

$-5y = -5$

$y = -5 \div -5$

$y = 1$

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$x + 4y = 2$

$x + 4(1) = 2$

$x + 4 = 2$

$x = 2 - 4$

$x = -2$

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Learn more

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