Tge following simultaneous equations are written in base two
11x + 10y=10001
10x+y=10
Solve the equation leaving your answer in base two.
double the 2nd equation and you have
11x + 10y = 10001
100x + 10y = 100
subtract to eliminate y.
-x = 1101
now finish it off
Don't know it
Let's solve the given system of equations step-by-step.
Step 1: Rewrite the equations in decimal form.
11x + 10y = 10001 ....... (Equation 1)
10x + y = 10 ....... (Equation 2)
Step 2: Solve Equation 2 for 'y'.
10x + y = 10
y = 10 - 10x
Step 3: Substitute the value of 'y' from Equation 2 into Equation 1.
11x + 10y = 10001
11x + 10(10 - 10x) = 10001
11x + 100 - 100x = 10001
-89x = 9901
x = 9901 / -89
x ≈ -111
Step 4: Substitute the value of 'x' into Equation 2 to find 'y'.
10x + y = 10
10(-111) + y = 10
-1110 + y = 10
y = 10 + 1110
y = 1120
Step 5: Convert the decimal values of 'x' and 'y' into binary form.
x = -111 ≈ -111₂
y = 1120 = 1110000000₂
Therefore, the solution to the given system of equations in base two is:
x = -111₂
y = 1110000000₂
To solve the given system of simultaneous equations in base two, we can use the standard method of simultaneous equations by substitution or elimination. Here, let's solve it using the elimination method.
Given equations:
Equation 1: 11x + 10y = 10001
Equation 2: 10x + y = 10
First, let's eliminate one variable from the equations. We will eliminate 'y' by multiplying Equation 2 by 10 and Equation 1 by 1:
10 * Equation 1: 110x + 100y = 100010
1 * Equation 2: 10x + y = 000010
Now, subtract the resulting equation (10 * Equation 2) from (1 * Equation 1) to eliminate 'y':
(110x + 100y) - (10x + y) = 100010 - 000010
110x - 10x + 100y - y = 100000
100x + 99y = 100000
So, we have a new equation:
Equation 3: 100x + 99y = 100000
Now, let's solve Equation 3 and Equation 2 together:
Equation 2: 10x + y = 10
Equation 3: 100x + 99y = 100000
Multiply Equation 2 by 100 to match the coefficients of 'x' in both equations:
100 * Equation 2: 1000x + 100y = 1000
Now, subtract the resulting equation (100 * Equation 2) from Equation 3 to eliminate 'x':
(100x + 99y) - (1000x + 100y) = 100000 - 1000
100x - 1000x + 99y - 100y = 99000
-900x - y = 99000
So, we have a new equation:
Equation 4: -900x - y = 99000
Now, rearrange Equation 4 to solve for 'y':
-y = 900x + 99000
y = -900x - 99000
Next, substitute the value of 'y' in terms of 'x' back into Equation 2:
10x + (-900x - 99000) = 10
Combine like terms and solve for 'x':
-890x - 99000 = 10
-890x = 10 + 99000
-890x = 99010
x = 99010 / -890
x ≈ -111
Now, substitute the value of 'x' back into Equation 2 to find 'y':
10(-111) + y = 10
-1110 + y = 10
y = 10 + 1110
y = 1120
The solution to the simultaneous equations in base two is approximately:
x ≈ -111 (base two)
y = 1120 (base two)