Solve the following system of equations:
x − 2y = 14
x + 3y = 9
There are multiple methods for solving systems of equations, but one common approach is to use substitution. Here's how it works for this system:
1. Solve one of the equations for one variable in terms of the other variable. Let's choose the first equation and solve for x:
x - 2y = 14
x = 2y + 14
2. Substitute the expression you found for x into the other equation, replacing x with 2y + 14:
x + 3y = 9
(2y + 14) + 3y = 9
3. Simplify and solve for y:
5y + 14 = 9
5y = -5
y = -1
4. Substitute this value of y back into one of the original equations and solve for x:
x - 2y = 14
x - 2(-1) = 14
x + 2 = 14
x = 12
Therefore, the solution to the system is (x,y) = (12,-1). You can verify this by plugging these values back into both equations and checking that they make true statements.