x + y=16
x - y=2
Leave ans in base 2
x + y = 16
x - y = 2
Adding the two equations together, we get:
2x = 18
Dividing both sides by 2, we get:
x = 9
Substituting this value back into either equation, we can solve for y:
9 - y = 2
Subtracting 9 from both sides, we get:
-y = -7
Dividing both sides by -1, we get:
y = 7
Therefore, the solution is x = 9 and y = 7.
To solve the system of equations, we can use the method of substitution.
Step 1: Solve one of the equations for one variable in terms of the other variable. Let's solve the second equation for x:
x - y = 2
Adding y to both sides:
x = 2 + y
Step 2: Substitute the expression for x in terms of y into the other equation.
x + y = 16
Using the expression for x from Step 1:
(2 + y) + y = 16
Simplifying:
2 + 2y = 16
Step 3: Solve the resulting equation for y.
2y = 16 - 2
2y = 14
y = 7
Step 4: Substitute the value of y back into one of the original equations to solve for x. Let's use the first equation:
x + y = 16
x + 7 = 16
x = 9
Therefore, the solution to the system of equations is x = 9 and y = 7.
Now, to express the answer in base 2, we convert each digit to its binary form.
For x = 9, its binary form is 1001.
For y = 7, its binary form is 0111.
Therefore, the solution in base 2 is x = 1001 and y = 0111.