If 8a−4b=20 and 4a−8b=4, then what is the value of a−b?
i got 2
easy way
8 a - 4 b = 20
4 a - 8 b = 4
-------------- add these
12 a - 12 b = 24
divide both sides by 12
a - b = 2
Well, it seems you already have the answer! If 8a - 4b = 20, and 4a - 8b = 4, you can solve the system of equations to find the values of a and b. But hey, why stop at just a minus b? Let's have some fun with math and turn it into a joke!
Why did the mathematician drown?
Because he couldn't keep his head above "a-b"!
To find the value of "a - b," we can use the given system of equations and solve for the values of 'a' and 'b.' Let's work step-by-step to find the solution:
1. Given equations:
8a - 4b = 20 ---(1)
4a - 8b = 4 ---(2)
2. Multiply equation (2) by -2 to make the coefficients of 'b' equal:
-2(4a - 8b) = -2(4)
-8a + 16b = -8 ---(3)
3. Add equations (1) and (3):
(8a - 4b) + (-8a + 16b) = 20 + (-8)
8a - 4b - 8a + 16b = 12b = 12
4. Divide both sides of the equation by 12:
12b/12 = 12/12
b = 1
5. Substitute the value of 'b' back into equation (1):
8a - 4(1) = 20
8a - 4 = 20
8a = 20 + 4
8a = 24
6. Divide both sides of the equation by 8:
8a/8 = 24/8
a = 3
Therefore, the value of "a - b" is:
a - b = 3 - 1 = 2
So, your answer is correct. The value of "a - b" is 2.
To find the value of a−b, we can use the given equations and solve for the values of a and b.
Given equations:
1) 8a−4b=20
2) 4a−8b=4
We can solve this system of equations using the method of elimination. We will eliminate one variable by multiplying one equation by a constant so that the coefficients of one of the variables will cancel out when the equations are added or subtracted.
Let's start by multiplying equation 2 by 2 to eliminate the a terms:
2 * (4a - 8b) = 2 * 4
8a - 16b = 8
Now we have the following equations:
1) 8a−4b=20
3) 8a−16b=8
By subtracting equation 3 from equation 1, we can eliminate a:
(8a - 4b) - (8a - 16b) = 20 - 8
8a - 4b - 8a + 16b = 12b = 12
12b = 12
Now we can solve for b:
b = 12 / 12
b = 1
To find the value of a, we can substitute the value of b into one of the given equations. Let's use equation 1:
8a - 4(1) = 20
8a - 4 = 20
8a = 20 + 4
8a = 24
a = 24 / 8
a = 3
Therefore, the value of a−b is:
a - b = 3 - 1 = 2.
So, you are correct. The value of a−b is indeed 2.