If it says use the method of substitution to solve the system of linear equations
3a=6-b
3a=4-b
How do i find the solution
Well, you use substitution. To do substitution, you choose one of the equations, and express one of the variables in terms of the other.
Actually, here, we can see that the first equation (3a = 6-b) can be readily substituted to the second equation (3a = 4-b), because of they have the same term, 3a:
If 3a = 6-b, and 3a = 4-b also, then
6-b = 4-b
6 = 4
which cannot be. If you arrive at this kind of answer (constant 1 = constant 2), that means there is no solution for this particular system of equations.
hope this helps~ `u`
To solve the system of linear equations using the method of substitution, we need to find a value for one variable in terms of the other variable from one equation, and then substitute that value into the other equation.
Let's start with the given system of equations:
1) 3a = 6 - b
2) 3a = 4 - b
From equation 1, we can express "b" in terms of "a" by subtracting 3a from both sides:
b = 6 - 3a
Now, we can substitute this value of "b" into equation 2:
3a = 4 - (6 - 3a)
We simplify the equation by distributing the negative sign inside the parentheses:
3a = 4 - 6 + 3a
Combine like terms:
3a - 3a = -2
Simplifying further, we get:
0 = -2
This equation is inconsistent since 0 cannot be equal to -2. Therefore, there is no solution to this system of equations.
In summary, by substituting the value of "b" from the first equation into the second equation, we find that the equations are inconsistent and have no solution.