solve the system by the elimination method -x+3y=5 -5x+15y=25
To solve the system using the elimination method, we need to eliminate one variable by multiplying one or both equations by appropriate numbers so that the coefficients of one variable are equal or opposite in both equations.
Let's start by multiplying the first equation by 5 to get rid of the coefficient of x in the second equation.
5(-x + 3y) = 5(5) -> -5x + 15y = 25
Now, we can see that the second equation has the same coefficients for x and y as the first equation. Now, we can subtract the first equation from the second equation to eliminate x.
(-5x + 15y) - (-5x + 3y) = 25 - 5
2y = 20
Simplifying, we get:
2y = 20
y = 10
Now that we have the value of y, we can substitute it back into the first equation to find x.
-x + 3(10) = 5
-x + 30 = 5
-x = 5 - 30
-x = -25
x = 25
Therefore, the solution to the system of equations is x = 25 and y = 10.