SOLUTION: If three times the first number plus four times the second number equals 26, and ten times the first number and minus two times the second number equals 10, what are the numbers?

Question 145978: If three times the first number plus four times the second number equals 26, and ten times the first number and minus two times the second number equals 10, what are the numbers?
Answer by ankor@dixie-net.com(22740) (Show Source): You can put this solution on YOUR website!
Let x = 1st number
Let y = 2nd number
:
Write an equation for each statement:
"If three times the first number plus four times the second number equals 26,"
3x + 4y = 26
:
"ten times the first number and minus two times the second number equals 10,"
10x - 2y = 10
:
what are the numbers?
;
We can use elimination here; multiply the 2nd equation by 2 and add to the 1st
20x - 4y = 20
3x + 4y = 26
-----------------adding eliminates y
23x + 0y = 46
x =
x = 2
:
Use the 1st equation to find y, (substitute 2 for x), Check the solutions in the 2nd equation.
RELATED QUESTIONS
If 5 times the first number plus three times the second number equals 47, and 10 times... (answered by Anthea Lawn)

If 5 times the first number plus three times the second number eaguals 47, and 10 times... (answered by checkley75)

two times a number plus three times another number equals 4.three times the first number... (answered by richwmiller)

The sum of three numbers is 10. Two times the second number minus the first number is... (answered by lwsshak3)

Please help me solve this word problem: If 5 times the first number plus three times... (answered by Edwin McCravy)

twice one number plus three times another equals -14. The first number minus 3 equals the (answered by ankor@dixie-net.com)

A number plus half of another number equals 6; twice the first number minus three times... (answered by josgarithmetic,greenestamps,ikleyn,MathTherapy)

i think of two numbers, the first number plus three times the second number is 1, the... (answered by Alan3354)

The first of two numbers minus four times a second number is at least -4. Three times the (answered by ankor@dixie-net.com)