use substitution method
m+2n=1 5m+3n=-23
please step by step so that i could understand
Substitution means we express one variable in terms of another, and substitute this expression into the second equation.
m+2n=1 ...(1)
5m+3n=-23 ...(2)
From (1), we have
m+2n=1
subtract 2n from each side to get
m+2n-2n=1-2n
m=1-2n ...(1a)
Substitute m from (1a) into (2) to get:
5m+3n=-23
5(1-2n)+3n=-23
5-10n+3n =-23
-7n = -23 -5
-7n = -28
n=(-28)/(-7)=4 ...(2a)
Substitute n from (2a) into (1a)
m=1-2n
=1-2*4
=-7
So m=-7, n=4
Last step!!
Substitute the values of m and n into equations (1) and (2) to verify that the solutions are correct:
m+2n=1 ...(1)
-7+2*4=-7+8=1 OK
5m+3n=-23 ...(2)
5*(-7)+3*4
=-35+12
=-23 OK
THANKS!!!!!!! great explaining!!!
Sure! To solve this system of equations using the substitution method, follow these steps:
Step 1: Solve one of the equations for one variable in terms of the other variable.
Let's solve the first equation, m + 2n = 1, for m in terms of n:
m = 1 - 2n
Step 2: Substitute the expression obtained in step 1 into the other equation.
Substitute m = 1 - 2n into the second equation, 5m + 3n = -23:
5(1 - 2n) + 3n = -23
Step 3: Simplify and solve the resulting equation.
Distribute 5 to both terms inside the parentheses:
5 - 10n + 3n = -23
Combine like terms:
-7n + 5 = -23
Step 4: Isolate the variable.
Subtract 5 from both sides:
-7n = -23 - 5
-7n = -28
Divide both sides by -7 to solve for n:
n = -28 / -7
n = 4
Step 5: Substitute the value of n back into one of the original equations to solve for the other variable.
Let's substitute n = 4 into the first equation, m + 2n = 1:
m + 2(4) = 1
m + 8 = 1
Subtract 8 from both sides:
m = 1 - 8
m = -7
Step 6: Check your solution by substituting the values of m and n into the other equation.
Substituting m = -7 and n = 4 into the second equation, 5m + 3n = -23:
5(-7) + 3(4) = -23
-35 + 12 = -23
-23 = -23
The solution to the system of equations is m = -7 and n = 4.