Question

""Solve the system using the elimination method and write out the linear combination you performed to eliminate one of the variables in the following system:

2m + n = 1
3m - 3n = 24

Show your work to find the values of ‘m’ and ’n.""

Answer 1

To solve the system using the elimination method, multiply the equations by appropriate factors to make the coefficients of one variable the same, and then subtract one equation from the other to eliminate that variable. The linear combination performed to eliminate 'n' is 3m + 21n = 3. Solve this equation to find the values of 'm' and 'n'. The solution to the system is 'm = 1' and 'n = 0'.

Step-by-step explanation:

To solve the system using the elimination method, we need to eliminate one of the variables when adding or subtracting the two equations. Let's eliminate the variable 'n'. Multiply the first equation by 3 and the second equation by 2 to make the coefficients of 'n' the same:

6m + 3n = 39m - 6n = 8

Now, subtract the second equation from the first equation:

6m + 3n - (9m - 18n) = 3m + 21n = 3

This is the linear combination we performed to eliminate the variable 'n'.

To find the values of 'm' and 'n', we can solve the simplified equation:

3m + 21n = 3

We can divide both sides by 3 to isolate 'm':

m + 7n = 1

Now, we can choose a value for 'n' and solve for 'm'. For example, let's choose 'n = 0':

m + 7(0) = 1

m = 1

So the solution to the system of equations is 'm = 1' and 'n = 0'.