A first number plus twice a second number is 1. Twice the first number plus the second totals 26. Find the numbers

Question

Help please............. ...................:::.

Answer 1

Let's call the first number X, and the second number Y.

 

A "first number" plus "twice a second number" is 1.

 

That translates to...

 

X + 2*Y = 1

 

"Twice the first number" plus "the second number" totals 26.

 

That translates to...

 

2*X + Y = 26

 

So now you have two equations to solve your two unknowns.

 

X + 2Y = 1

2X + Y = 26

 

Multiply the first equation by -2 and add the rows.

 

-2X - 4Y = -2

 2X + Y = 26

____________

      -3Y = 24

 

Y = -8

 

Since 2X + Y = 26

 

2X - 8 = 26

2X = 34

X = 17

 

So the first number is 17, and the second number is -8.

 

Check your work!!

 

A number (17) + twice the second number (2*-8 = -16) is 1.

17 - 16 is indeed 1.

 

Twice the first number (2*17 = 34) + the second number (-8) totals 26.

34 - 8 is indeed 26.