How many solutions are there to the following system of equations?

3x + 7y = –10
15x + 35y = –45

Question

How many solutions are there to the following system of equations?

3x + 7y = –10
15x + 35y = –45

raden · Answer

what do you think about :
3/15 .... 7/35 ..... -10/-45 ?

anonymous · Answer

the two lines are parallel but there are no solutions because the coefficients don't match up.

anonymous · Answer

so the lines are parallel, but distinct

nightmarenight · Answer

So it's 0? no solution isnt an option...

anonymous · Answer

no solution

anonymous · Answer

well, no solution would be a better answer, but if no solution is not an option, then i might go with 0

anonymous · Answer

Use either equation to solve for one variable in terms of another. I will use the first equation to solve for x in terms of y.
$$3x+7y=-10$$$$3x=-7y-10$$$$x=\frac{-7}{3}y-\frac{10}{3}$$Now replace x in the second equation with this new expression.$$15x+35y=-45$$$$15(-\frac{7}{3}y-\frac{10}{3})+35y=-45$$$$-35y-50+35y=-45$$The -35y and 35y cancel out so you get:$$-50=-45$$When is -50 equal to -45? Never. So there is no solution. (zero solutions)