the sum of two numbers is 38.the greater number is 8 more than the other number.find each number.use a system of linear equations to justify your answers.
x+y=38
y=x+8
X=15
Y=23
Let's call the two numbers x and y.
From the given information, we can create two equations:
1) The sum of the two numbers is 38:
x + y = 38
2) The greater number is 8 more than the other number:
x = y + 8
To solve this system of equations, we can use the substitution method or the elimination method. Let's use the substitution method:
Start with equation 2) and solve it for y:
x = y + 8
y = x - 8
Now substitute this value of y into equation 1):
x + y = 38
x + (x - 8) = 38
2x - 8 = 38
Add 8 to both sides:
2x = 46
Divide by 2:
x = 23
Now substitute this value of x back into equation 2) to find y:
y = x - 8
y = 23 - 8
y = 15
So the two numbers are x = 23 and y = 15.
To find the two numbers, let's assign variables to represent them. Let's call the smaller number "x" and the greater number "y."
According to the given information:
1) The sum of the two numbers is 38, which can be written as: x + y = 38.
2) The greater number is 8 more than the other number, which can be expressed as: y = x + 8.
Now, we have a system of linear equations. We can use the method of substitution or elimination to solve this system.
Let's use the substitution method:
1) Substitute the value of y from the second equation into the first equation:
x + (x + 8) = 38.
2) Simplify the equation:
2x + 8 = 38.
3) Subtract 8 from both sides of the equation:
2x = 38 - 8.
4) Simplify further:
2x = 30.
5) Divide both sides of the equation by 2:
x = 15.
Now that we have the value of x, we can substitute it back into either of the original equations. Let's substitute it into equation 2:
y = x + 8,
y = 15 + 8,
y = 23.
So, the smaller number (x) is 15, and the greater number (y) is 23.
To summarize:
The smaller number is 15, and the greater number is 23.