the sum of a numbers is 15 and their difference is 4. form a pair of simultaneous equations and solve to find the numbers.
x+y=15
x-y=4
it does not matter if x bigger or y bigger
add
2x + 0 = 19
x = 8.5
then
8.5 + y = 15
y = 4.5
To form a pair of simultaneous equations, let's denote the two numbers as x and y.
Based on the given information, we can form the following equations:
1. The sum of the two numbers is 15:
x + y = 15
2. The difference between the two numbers is 4:
x - y = 4
To solve these simultaneous equations, we can use the method of substitution or elimination. Let's use the method of substitution:
From equation 1, isolate one variable in terms of the other. For example, isolate y:
y = 15 - x
Now substitute this value of y into equation 2:
x - (15 - x) = 4
x - 15 + x = 4
2x - 15 = 4
2x = 4 + 15
2x = 19
Divide both sides by 2 to solve for x:
x = 19/2
x = 9.5
Now substitute the value of x back into either equation 1 or 2 to solve for y. Let's use equation 1:
9.5 + y = 15
y = 15 - 9.5
y = 5.5
So the two numbers that satisfy the given conditions are x = 9.5 and y = 5.5.