How do you find the solution of the system of equations #x+3y=12# and #x-y=4#?

x + 3y = 12 (1)

x - y = 4 (2)

(1) gives x = 12 - 3y. Replace x by (12 - 3y) into (2):

12 - 3y - y = 4 -> -4y = -8 -> y = 2

x = 12 - 3(2) = 6

Check: (1): 6 + 6 = 12. Correct

(2) : 6 - 3 = 4. Correct

To find the solution of the system of equations (x+3y=12) and (x-y=4), you can use the method of substitution or elimination.

Using the substitution method:

1. Solve one of the equations for either (x) or (y).
2. Substitute the expression obtained in step 1 into the other equation.
3. Solve for the remaining variable.
4. Substitute the value found in step 3 into one of the original equations to find the value of the other variable.
5. Check the solution by substituting the values of (x) and (y) into both original equations.

Using the elimination method:

1. Add or subtract the two equations to eliminate one of the variables.
2. Solve the resulting equation for one of the variables.
3. Substitute the value found in step 2 into one of the original equations to find the value of the other variable.
4. Check the solution by substituting the values of (x) and (y) into both original equations.