Twice a number plus three times a second number is twenty two. Three times the first number plus four times the second is thirty-one. Find the numbers.

Short Answer

Expert verified

First number is 5 and second number is 4

Step by step solution

01

Given Information 

Twice a number plus three times a second number is twenty two. Three times the first number plus four times the second is thirty-one

02

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 twenty two

2x+3y=22

Three times the first number plus four times the second is thirty-one

3x + 4y=31

03

Solve both the equations

2x+3y=22x=22-3y23x+4y=31322-3y2+4y=3166-9y2+8y2=3166-1y2=3166-1y=62-1y=62-66-1y=-4y=4x=22-3y2x=22-3(4)2x=5

Two numbers are 4 and 5

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