If x-2y=-5 and -7x-6y = 8 are true equations, what would be the value of -6x - 8у?
To find the value of -6x - 8y, we first need to solve the given system of equations:
Equation 1: x - 2y = -5
Equation 2: -7x - 6y = 8
We can start by multiplying Equation 1 by -7 to make the coefficients of x match in both equations:
-7(x - 2y) = -7(-5)
-7x + 14y = 35
Now we have the equations:
-7x + 14y = 35
-7x - 6y = 8
Subtracting the second equation from the first equation (eliminating x):
(-7x + 14y) - (-7x - 6y) = 35 - 8
-7x + 14y + 7x + 6y = 27
20y = 27
y = 27/20
Now, substitute the value of y into Equation 1:
x - 2(27/20) = -5
x - (54/20) = -5
x - (27/10) = -5
x = -5 + 27/10
x = -50/10 + 27/10
x = -23/10
Therefore, the solution to the system of equations is x = -23/10 and y = 27/20.
Now, to find the value of -6x - 8y:
-6(-23/10) - 8(27/20)
= 138/10 - 216/20
= 138/10 - 108/10
= 30/10
= 3
So, the value of -6x - 8y is 3.