To solve this system of equations, we can use the method of elimination. The goal is to eliminate one of the variables, such as x or y, by adding or subtracting the equations.
First we can eliminate the y variable by adding the two equations together:
X + 3y = 14
2x - 3y = -8
3x = 6
Dividing both sides by 3:
x = 2
Now we have the value of x, we can substitute it back into one of the original equations:
X+3y=14
2 + 3y = 14
Subtracting 2 from both sides:
3y = 12
Dividing both sides by 3:
y = 4
So the solution of the system of equations is (x,y) = (2,4)
To check the solution, we can substitute the values back into the original equations:
x + 3y = 14
2 + 3(4) = 14
2 + 12 = 14
14 = 14
and
2x - 3y = -8
2(2) - 3(4) = -8
4 - 12 = -8
-8 = -8
As the equation holds true, the solution (2,4) is correct.