2m+n=3
3m+4n=2
In Elimination method
8m+4n=12
3m+4n=2
subtract to get
5m = 10
...
Thanks off to school tomorrow
In elimination method, the goal is to eliminate one variable at a time by adding or subtracting the given equations. Here's how you can solve the given system of equations using the elimination method:
Step 1: Multiply one or both equations by suitable constants to make the coefficients of one of the variables the same, but with opposite signs in both equations. This will allow you to add or subtract the equations to eliminate that particular variable.
In this case, let's try to eliminate the variable "n." To do that, we can multiply the first equation by 4 and the second equation by -1, so that the coefficients of "n" have opposite signs.
Equation 1: 2m + n = 3 (multiply by 4)
4(2m + n) = 4(3)
8m + 4n = 12 (equation 3)
Equation 2: 3m + 4n = 2 (multiply by -1)
-1(3m + 4n) = -1(2)
-3m - 4n = -2 (equation 4)
Step 2: Add the modified equations (equation 3 and equation 4) to eliminate the "n" variable.
(8m + 4n) + (-3m - 4n) = 12 + (-2)
8m - 3m + 4n - 4n = 10
5m + 0 = 10
5m = 10
m = 10/5
m = 2
Step 3: Substitute the value of m (found in step 2) back into one of the original equations to find the value of the remaining variable.
Using equation 1:
2(2) + n = 3
4 + n = 3
n = 3 - 4
n = -1
So, the solution to the system of equations is m = 2 and n = -1.