Answer: 3 and 14
Step-by-step explanation:
Let the two numbers be X and Y.
"The sum of twice a number and 7 times another number is 49:"
2X + 7Y = 49
"The first number decreased by 3 times the second number is 5:"
X - 3*Y = 5
Rewrite the second equation so that either the X or Y is isolated. I'll choose X:
X = 5+3Y
Now use this definition of X in the first equation:
2X + 7Y = 49
2(5+3Y) +7Y = 49
10 + 6Y + 7Y = 49
13Y = 39
Y = 3
Use Y = 3 to solve for X:
X - 3*Y = 5
X - 3*3 = 5
X = 5 + 9
X = 14
The values are X = 14 and Y = 3.
Check to see if these work:
2X + 7Y = 49
Does 2(14) + 7(3) = 49 ??
28 + 21 = 49 ? YES
X - 3*Y = 5
Does 14 - 3*(3) = 5 ???
14 - 9 = 5 YES
