Solve the system using elimination.
5x-5y=10 and x-5y= -14
subtract the equations (to eliminate y)
solve for x , then substitute back to find y
To solve the system of equations using elimination, we need to eliminate one variable by adding or subtracting the equations.
In this case, we can eliminate the variable "x" by subtracting the second equation from the first equation.
(5x - 5y) - (x - 5y) = 10 - (-14)
Simplifying the equation, we get:
5x - 5y - x + 5y = 10 + 14
Combining like terms, we have:
4x = 24
Next, we isolate the variable "x" by dividing both sides of the equation by 4:
4x/4 = 24/4
x = 6
Now that we have found the value of "x," we substitute it back into one of the original equations to find the value of "y." Let's use the second equation:
x - 5y = -14
Substituting x = 6, we get:
6 - 5y = -14
Next, we isolate the variable "y" by moving the constant term to the other side of the equation:
-5y = -14 - 6
-5y = -20
To solve for "y," we divide both sides of the equation by -5:
-5y / -5 = -20 / -5
y = 4
Therefore, the solution to the system of equations is x = 6 and y = 4.