Question

If 2x + 3y = 17 and 3x + 4y = 24, then 5x +7y =

7
41
3
-7
-41

Answer 1

I'll use the first one
2x+3y=17 => 2x=17-3y => x=17-3y/2
now put this new equation into the second one
3x+4y=24 => 3((17-3y)/2)+4y=24
now to work it out.
(51-9y)/2+4y=24
so (51/2)-(9y/2) +4y=24
then (-9y/2)+4y=24-(51/2)
-4.5y+4y=24-25.5
(-1/2)y=-3/2
y=(-3/2)/(-1/2)
y=3
when y=3 find x by putting 3 were y is
3x+4y=24
3x+4(3)=24
3x+12=24
3x+24-12 => 3x=12
therefore x=4
now that y=3 and x=4