find two numbers whose sum is 64 and whose difference is 42?

Question

Solve the problem by using systems of equations.

Answer 1

X + Y = 64
X - Y = 42

add them together to get:

2X = 106
so X = 53
so Y = 11

Answer 2

Let the two numbers be x and y.

Their sum is 64: x + y = 64

And their difference is 42: x - y = 42

Solve for x in both equations:

x + y = 64
x = 64 - y

x - y = 42
x = 42 + y

Combine the equations:
64 - y = 42 + y
64 - 42 = y + y
22 = 2y
y = 11

Substitute y = 11

x = 64 - y = 64 -11 = 53

Check the other equation:

x = 42 + y = 42 + 11 = 53

Therefore, x = 53 and y = 11

Answer 3

The Linear System Is As Follows
X+Y=64
X-Y=42

add both lines together

2x=106 therefore X=53

put X into any equation that you want
X+Y=64 and X=53 therefore Y=11

Check Another equation to see your answer is right

53-11=42

therefore the solution set is {53,11}

you could have used matrices and bring the matrix into row echelon form but dont need to make it hard

good luck !

Answer 4

(64+42)/2 = 53, the larger number
64-53 = 11, the smaller number.
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Mental math: The sum of the two numbers divided by 2 is the larger number, and then you can find the smaller number by subtracting the larger number from the sum.

Answer 5

Let A & B represent the two numbers, A is the larger.
A+B=64
A-B=42
Add both together:
2A=106
A=53
Substitute in the first:
53+B=64
B=64-53
B=11
Proof, using second equation:
A-B=42
53-11=42
LHS=RHS

Answer 6

x+y=64
x-y=42

x=53, y=11