Identify the solution(s) of the system of equations, if any.
x + 5y = 7
4x - 5y = 13
if you add the two equations, you get
5x = 20
I think you can solve that, eh?
To find the solution(s) of the system of equations, you can solve them using either the substitution method or the elimination method. Let's solve it using the elimination method.
First, we'll multiply the first equation by 4 to eliminate the x term.
4(x + 5y) = 4(7)
4x + 20y = 28
Now we can line up the equations to eliminate the x terms:
4x + 20y = 28
4x - 5y = 13
Subtracting the second equation from the first, we can eliminate the x term:
(4x + 20y) - (4x - 5y) = 28 - 13
4x + 20y - 4x + 5y = 15
25y = 15
Dividing both sides by 25, we get:
y = 15 / 25
y = 3 / 5
Now we substitute the value of y back into one of the original equations, let's use the first equation:
x + 5(3/5) = 7
x + 3 = 7
x = 7 - 3
x = 4
Therefore, the solution to the system of equations is x = 4 and y = 3/5.