Question

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

plus four times the second number is two. Find the numbers

Short answer

First number is -2 and second number is 1

Step-by-step solution

Given Information 

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

plus four times the second number is two.

Assume variables and frame equations

Let 'x' be the first number and 'y' be the second number

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

2x +3y=-1

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

x +4y=2

Solve equations

$$\begin{gathered} 2x\hspace{0.17em}+3y=-1\hspace{0.17em} \\ \hspace{0.17em}x\hspace{0.17em}+4y=2 \\ x=2-4y \\ Substituteitinfirstequation \\ 2\left(2-4y\right)\hspace{0.17em}+3y=-1\hspace{0.17em} \\ 4-8y+3y=-1 \\ 4-5y=-1 \\ -5y=-5 \\ y=1 \\ x=2-4y \\ x=2-4\left(1\right) \\ x=-2 \end{gathered}$$

first number is -2 and second number is 1