How do you find the intersection of the lines 5x + 2y = 60 and 3x + 2y = 45?
you can find it one of two ways.
the first is using the calculator which is the easiest or you can do it by hand.
calculator:
solve for y for both equations and then plug the first equation as y1 and the second equation as y2. then you do 2nd calc intersection (5) on the calc [if you own a TI graphing calculator]
5x+2y=60
2y=-5x+60
y=(-5/2)x+30
3x+2y=45
2y=-3x+45
y=(-3/2)x+22.5
y1=(-5/2)x+30
y2=(-3/2)x+22.5
press [2nd] (blue button)
press [calc] (second from top rightest button named "trace")
press [5] (intersection)
press [enter]
press [enter]
and it will show you the x and y values of the intersection
by hand:
take the two equations solved for y from above. put them equal to each other and solve for x. then plug the solution for x into one of the equations to find y
(-5/2)x+30=(-3/2)x+22.5
(-2/2)x=-7.5
x=7.5
5x + 2y = 60
5(7.5)+2y=60
2y=22.5
y=11.25
can check this y by plugging x into the other equation as well
3x + 2y = 45
3(7.5)+2y=45
2y=22.5
y=11.25
therefore, the intersection is at
(7.5, 11.25)