To solve this system of two linear equations, we'll use the method of substitution or elimination. First, let's list our system of equations:
1. dx + 6y = -14
2. -10x - 4y = -11
We need to isolate one variable in one of the equations so that we can substitute or eliminate. Let's rearrange equation 2 for x:
x = -4y/10 - 11/10
Now we can substitute this equation into equation 1, replacing x:
d(-4y/10 - 11/10) + 6y = -14
This simplifies to dy/2 - (11/10)d + 6y = -14. Then solve for d by simplifying and isolating the variable:
dy/2 = (11/10)d + 14 - 6y
To make the calculation easier, multiply every term in the equation by 2 to clear the fraction:
d*y = (22/10)d + 28 - 12y
d = (28 - 12y)/(y - 22/10)
We have a solution in terms of y. However, we don't yet have a value for y. To find a numerical value for d, we would need to solve for y in our system of equations.
First, substitute the rearranged equation 2 (-10x - 4y = -11) into equation 1:
d(-4y/10 - 11/10) + 6y = -14
By solving this equation, we can find the value of y, and then substitute it into our solution for d. Then, we will get an answer for the value of d that makes the system of equations true.
Without the numerical solution, we cannot directly conclude the value of d. It keeps dependent on the value of y.