Need help with algebra equation

[JBridges]

Please explain how I should do this:
Suppose you solve the system below by multiplying first equation by d and the second equation by b and then subtracting.

ax+by=p
cx+dy=q

a.What is the coefficient of x in the resulting equation? Solve the equation for x
b.State a relationship among the numbers a,b,c,and d that guarantees that the system does not have exactly one solution.

Thanks so much!

 

[mark07]

The problem is explaining you what to do. Please show your work for at least the first step

... multiplying first equation by d and the second equation by b and then subtracting.

which simply answers part (a), and then we can help you with part (b).

I promise you'll get more out of it then...

 

[JBridges]

maybe I was absent that day but I cannot figure out how to start it off.

 

[mark07]

a) Multiply 1st equation by d, 2nd by b:

\(\displaystyle \L dax+dby=dp\)

\(\displaystyle \L bcx+bdy=bq\)

Subtract 2nd from 1st, simplify:

\(\displaystyle \L (dax+dby) - (bcx+bdy) = dp - bq\)

\(\displaystyle \L dax+dby - bcx-bdy = dp - bq\)

\(\displaystyle \L dax - bcx = dp - bq\)

\(\displaystyle \L (da - bc)x = dp - bq\)

\(\displaystyle \L x=?\)

 

[mark07]

b) Look at the equation from above,

\(\displaystyle \L (da - bc)x = dp - bq\)

What happens when \(\displaystyle \L (da - bc)=0\) ?