Given that 2a+b=5 and a +2b=4= find the value of a
To solve for the value of a and b, we can use the method of substitution.
From the first equation, we know that 2a + b = 5. We can rearrange this equation to solve for b:
b = 5 - 2a
Now we substitute this expression for b in the second equation:
a + 2(5 - 2a) = 4
Simplifying this equation:
a + 10 - 4a = 4
Combining like terms:
-3a + 10 = 4
Subtracting 10 from both sides of the equation:
-3a = -6
Dividing both sides by -3:
a = 2
Therefore, the value of a is 2.
To find the value of "a" from the given equations, we can use the method of substitution or elimination. Let's solve it using the substitution method:
Step 1: Solve one of the given equations for one variable in terms of the other.
From the equation 2a + b = 5, we can solve for b in terms of a:
b = 5 - 2a
Step 2: Substitute the expression found in step 1 into the other equation.
Substituting b = 5 - 2a into the equation a + 2b = 4, we get:
a + 2(5 - 2a) = 4
Step 3: Simplify the equation and solve for a.
a + 10 - 4a = 4
10 - 3a = 4
10 - 4 = 3a
6 = 3a
a = 6/3
a = 2
So, the value of a is 2.