Solve without using any fractions
7m+2n = 20
2m=3n-5
To solve this system of equations without using fractions, we can first isolate a variable in one of the equations and substitute it into the other equation.
From the second equation, we can isolate m:
2m = 3n - 5
Divide both sides by 2:
m = (3n - 5) / 2
Substitute this expression for m into the first equation:
7m + 2n = 20
7[(3n - 5) / 2] + 2n = 20
Multiply both sides by 2 to get rid of the fraction:
7(3n - 5) + 4n = 40
21n - 35 + 4n = 40
Combine like terms:
25n - 35 = 40
Add 35 to both sides:
25n = 75
Divide both sides by 25 to isolate n:
n = 3
Now substitute this value of n back into the expression for m:
m = (3n - 5) / 2
m = (3(3) - 5) / 2
m = (9 - 5) / 2
m = 4 / 2
m = 2
So the solution to the system of equations is m = 2 and n = 3.