Question

Use the elimination method or substitution method to solve the system of linear equations.

2m+4=3n
5m−3n=−1

m= ?
n= ?

Answer 1

We can use the substitution method to solve this system of linear equations.

First, we can rearrange the first equation to solve for one of the variables in terms of the other:

2m + 4 = 3n

2m = 3n - 4

m = (3/2)n - 2

Next, we can substitute this expression for m into the second equation:

5m - 3n = -1

5((3/2)n - 2) - 3n = -1

Simplifying this equation, we get:

(15/2)n - 10 - 3n = -1

(9/2)n = 9

n = 2

Now that we know the value of n, we can substitute it back into either of the original equations to solve for m. Using the first equation, we get:

2m + 4 = 3n

2m + 4 = 3(2)

2m + 4 = 6

2m = 2

m = 1

Therefore, the solution to the system of equations is m = 1 and n = 2.