4x-y=-5 and x-5y=-4 equate each compoent on each side of the equation simplfy
find out what x and y is
To solve the system of equations 4x - y = -5 and x - 5y = -4, we can use the method of substitution or elimination.
Method 1: Substitution
From the second equation, we can solve for x in terms of y:
x - 5y = -4
x = 5y - 4
Substitute this expression for x in the first equation:
4x - y = -5
4(5y - 4) - y = -5
20y - 16 - y = -5
19y - 16 = -5
19y = 11
y = 11/19
Substitute y = 11/19 back into x = 5y - 4 to find x:
x = 5(11/19) - 4
x = 55/19 - 76/19
x = -21/19
Therefore, the solution for the system of equations is x = -21/19 and y = 11/19.
Method 2: Elimination
Multiply the second equation by 4 and the first equation by 1 to make the coefficients of x the same:
4(x - 5y) = 4(-4)
4x - 20y = -16
Now we can subtract this equation from the first equation to eliminate x:
(4x - y) - (4x - 20y) = (-5) - (-16)
4x - y - 4x + 20y = -5 + 16
19y = 11
y = 11/19
Substitute y = 11/19 back into the first equation to find x:
4x - (11/19) = -5
4x = -5 + 11/19
4x = -95/19 + 11/19
4x = -84/19
x = -21/19
Again, the solution for the system of equations is x = -21/19 and y = 11/19.