Answer:
Explanation:
x-6y=4
To solve these equations, we can use the elimination method. We want to eliminate one of the variables, either x or y, by multiplying one of the equations by a constant so that the coefficients of one variable will be the same in both equations but with opposite signs. For example, we can multiply the first equation by 4 to get:
-20x - 24y = -128
Then we can add this equation to the second equation to eliminate y:
-20x - 24y + 4x - 6y = -128 + 4
Simplifying this equation gives:
-16x - 30y = -124
Now we can isolate one variable in terms of the other:
-16x - 30y = -124
-16x = 30y - 124
x = (30/(-16))y + (-124/(-16))
x = (-15/8)y + 31/2
We can substitute this expression for x into either of the original equations to solve for y. For example, substituting into the first equation gives:
-5((-15/8)y + 31/2) - 6y = -32
Multiplying by -8 to clear the fractions gives:
75y - 248 - 48y = 256
Simplifying and solving for y gives:
27y = 504
y = 18.67
Then we can substitute this value of y back into our expression for x to find:
x = (-15/8)(18.67) + 31/2
x = -12.25
Therefore, the solution to the system of equations is:
x = -12.25
y = 18.67