solve by the substitution method
2m+n=9
m-6n=50
the solution is (___,___)
1. 2m + n = 9
m - 6n = 50
Using Eq.1, solve for n:
n = 9 - 2m
Substitute 9 - 2m for n in Eq. 2:
m -6(9 -2m) = 50
Solve for m:
m - 54 + 12m = 50
m = 8
Substitute 8 for m in Eq. 1:
2(8) + n = 9
n = -7.
Solution: m = 8, and n = -7.
x=8-4y,3x+5y=3
To solve the system of equations using the substitution method, we'll start by solving one of the equations for one variable and substituting it into the other equation.
Let's solve the second equation for m:
m - 6n = 50
m = 50 + 6n
Now we'll substitute this expression for m into the first equation:
2(50 + 6n) + n = 9
Distribute the 2:
100 + 12n + n = 9
Combine like terms:
13n + 100 = 9
Subtract 100 from both sides:
13n = -91
Divide by 13:
n = -91/13
Simplify:
n = -7
Now, substitute the value of n back into one of the original equations to find the value of m:
2m + n = 9
2m + (-7) = 9
2m - 7 = 9
Add 7 to both sides:
2m = 16
Divide by 2:
m = 8
Therefore, the solution to the system of equations is (8, -7).