Respuesta :
Answer:
first number(x) = 2 second number(y)= 6
Step-by-step explanation:
This is an example of a simultaneous equation.
First write this word problem as equations, where x is the "first number" that you've mentioned and y is the "second number".
x + 2y = 14 (equation 1)
2x + y = 10 (equation 2)
This is solved using the elimination method.
We need to make one of the coefficients the same - in this case we can make y the same. In order to do this we need to multiply equation 2 by 2, so that y becomes 2y.
2x + y = 10 MULTIPLY BY 2
4x + 2y = 20 (this is now our new equation 2 with the same y coefficient)
Now subtract equation 1 from equation 2.
4x - x + 2y - 2y = 20 - 14 (2y cancels out here)
3x = 6
x = 2
Now we substitute our x value into equation 1 to find the value of y.
2 + 2y = 14
2y = 12
y = 6
Hope this has answered your question.
Answer:
6 and 2
Step-by-step explanation:
Let the first number =a
Let the second number =b
A first number plus twice a second number is 14.
- a+2b=14
Twice the first number plus the second totals 10.
- 2a+b=10
We solve the two equations simultaneously
[tex]a+2b=14 \implies a=14-2b\\$Substitute into the second equation$\\2(14-2b)+b=10\\28-4b+b=10\\-3b=10-28\\-3b=-18\\b=6[/tex]
Recall:
a=14-2b
=14-2(6)
=14-12
a=2
The two numbers are 6 and 2.