the sum of 2 numbers is 31 and the difference is 7 what are the 2 numbers
Make a system of equations:
x+y=31; x-y=7
Solve the left one:
x=7+y
Substitute for the right equation:
7+y+y=31
7+2y=31
2y=24
y=12
Solve x+12=31
x=19
So the two numbers are 19 and 12
When I say "Solve for the left one", that should say "Solve for the right one"
To find the two numbers, we can set up a system of equations based on the given information.
Let's call the first number x and the second number y.
From the given information, we know two things:
1. The sum of the two numbers is 31: x + y = 31.
2. The difference between the two numbers is 7: x - y = 7.
To solve this system of equations, we can use the method of substitution or elimination.
Let's solve it using the substitution method:
1. Rearrange the first equation to solve for x: x = 31 - y.
2. Substitute this value of x into the second equation: (31 - y) - y = 7.
3. Simplify the equation: 31 - 2y = 7.
4. Solve for y: 31 - 7 = 2y, y = 12.
5. Substitute the value of y back into the first equation to find x: x + 12 = 31, x = 19.
Therefore, the two numbers are 19 and 12.