# how to find the points of intersection

my question is find the points of intersection of the straight lines with equations x + 2y = -5 and 3x - y = 13 ? but i have no idea how to do it please help i am revising for my maths standard grade exam !!

ok so this is basically a case of simultaneous equations.... and there are two methods. The first is where you substitute one equation into another.
chloe
14 April 2011
So if we take the first equation: x +2y=-5 and we re-arrange it to get x on its own then we have x=-5-2y
chloe
14 April 2011
sorry that should be 3(-5-27)-y=13
chloe
14 April 2011
Then we can substitute this value into the second equation so we have 3(-5-2y) = 13
chloe
14 April 2011
and then simplify to get -15-7y=13
chloe
14 April 2011
so we expand it to get -15-6y-y=13
chloe
14 April 2011
aah typos! It should be 3(-5-2y)-y=13
chloe
14 April 2011
then we divide both sides by -7 so that y=-4
chloe
14 April 2011
now we have to find out what y is so the first step is to add 15 to both sides to get -7y=28
chloe
14 April 2011
Now all we have to do is substitue this value back into either one of the first equation to find out what x is
chloe
14 April 2011
so the point of intersection is (3.-4)
chloe
14 April 2011
x=3
chloe
14 April 2011
x-8=-5
chloe
14 April 2011
so x +(2 x-4) = -5
chloe
14 April 2011
The second method is to subtract one equation from another but for that you need to have equal numbers of x or y in both equations (which you don't have here)
chloe
14 April 2011