Identify the solution(s) of the system of equations, if any.
x+5y=5
2x-15y=0
Multiply first equation by 2.
2x + 10y = 10
2x - 15y = 0
Subtract second equation from first.
25y = 10
y = 10/25 = 2/5 = .4
Insert that value into the first equation and solve for x. Check by inserting both values into the second equation.
To solve the system of equations, you can use either the substitution method or the elimination method. Let's use the elimination method to find the values of x and y.
Multiply the first equation by 2:
2(x + 5y) = 2(5)
2x + 10y = 10
Now you have the following system of equations:
2x + 10y = 10
2x - 15y = 0
Next, subtract the second equation from the first equation to eliminate the x terms:
(2x + 10y) - (2x - 15y) = 10 - 0
2x + 10y - 2x + 15y = 10
25y = 10
Divide both sides of the equation by 25 to solve for y:
25y/25 = 10/25
y = 2/5
Now substitute the value of y back into one of the original equations to solve for x. Let's use the first equation:
x + 5(2/5) = 5
x + 2 = 5
x = 5 - 2
x = 3
Therefore, the solution to the system of equations is x = 3 and y = 2/5.