Solve by either the substitution method or the addition or subtraction method
2m=n-3
3m=2n-9
Just replace n with (2m + 3) in the second equation. Then solve for m. Once you know the value of m, use either of your equations, such as n = 2m+3, to get n.
To solve the given system of equations using the substitution method, we start by solving one of the equations for one variable and then substituting that expression into the other equation.
Let's solve the first equation, 2m = n - 3, for n:
n = 2m + 3
Now we substitute this expression for n in the second equation, 3m = 2n - 9:
3m = 2(2m + 3) - 9
Next, simplify the equation by distributing the 2 to the terms inside the parentheses:
3m = 4m + 6 - 9
Combine like terms:
3m = 4m - 3
To isolate the variables, subtract 4m from both sides of the equation:
3m - 4m = -3
-m = -3
Now divide both sides of the equation by -1 to solve for m:
m = -3 / -1
m = 3
Once we have the value of m, we can substitute it back into one of the original equations to solve for n. Let's use n = 2m + 3:
n = 2(3) + 3
n = 6 + 3
n = 9
Therefore, the solution to the system of equations is m = 3 and n = 9.