use substitution to solve the system of equations
4x+2y=14
3x-5y =-22
use elimination to solve the system of equations
2x+3y=15
x-3y=3
Substitution:
From the first equation, solve for x in terms of y:
4x + 2y = 14
4x = 14 - 2y
x = (14 - 2y)/4
x = 7/2 - y/2
Now substitute x in the second equation:
3(7/2 - y/2) - 5y = -22
21/2 - 3y/2 - 5y = -22
21 - 3y - 10y = -44
21 - 13y = -44
-13y = -65
y = 5
Now substitute y back into x:
x = 7/2 - 5/2
x = 1
Therefore, the solution to the system of equations is x = 1 and y = 5.
Elimination:
Add the two equations to eliminate y:
2x + 3y + x - 3y = 15 + 3
3x = 18
x = 6
Substitute x back into one of the original equations to solve for y:
x - 3y = 3
6 - 3y = 3
-3y = -3
y = 1
Therefore, the solution to the system of equations is x = 6 and y = 1.