a first number plus twice the second number is 10 twice the first number plus the second totals 23 find the numbers? What is the smaller of the two numbers

Answer 1

a first number plus twice the second number is 10 twice the first number plus the second totals 23 find the numbers? What is the smaller of the two numbers

First # = X

Second # = Y

X + 2Y = 10

2X + Y = 23

We can use substitution or elimination:

Substitution:

solve for x in the first equation:

X = 10 - 2Y

substitute for X in the 2nd equation:

2(10 - 2Y) + Y = 23

solve for y:

20 -4Y + Y = 23

20 - 3Y = 23

-3Y = 3

Y = -1

Sub Y=-1 in either equation to solve for X:

X = 10 - 2(-1)

X = 10 + 2

X = 12

Answer: The larger of the 2 numbers is 12, the smaller is -1.