Use addition to solve the linear system of equations.
Y=3x+1
Y=2x-4
To use addition to solve this system, we need to add the two equations together in a way that will eliminate one of the variables.
We can do this by adding the left sides of the equations together, and then adding the right sides of the equations together:
Y + Y = (3x+1) + (2x-4)
Simplifying this, we get:
2Y = 5x - 3
Now we can solve for Y:
Y = (5x-3)/2
To solve for x, we can substitute this value of Y into one of the original equations (let's use the first one):
Y = 3x+1
(5x-3)/2 = 3x+1
Multiplying both sides by 2 to clear the fraction, we get:
5x - 3 = 6x + 2
Subtracting 5x from both sides, we get:
-3 = x + 2
Subtracting 2 from both sides, we get:
x = -5
So the solution to the system is (x,y) = (-5, -14).