how do you figure out where 2 equations intersect (5s+2t=6) (9s+2t=22)

Question

im having trouble figuring out at what point do two equations intersect

Answer 1

5s+2t=6

9s+2t=22

subtract 1st from 2nd above to get

9s-5s = 22-6

4s = 16

s = 16/4 = 4

5(4)+2t =6

2t = 6-20=-14

t =-14/2 =-7

s=4, t=-7

Answer 2

These two equations together form a system of equations. You can graph them (try Desmos Graphing Calculator website). Or, use algebra, as follows:

5s + 2t = 6

9s + 2t = 22

There are two methods: substitution and elimination. In this example, the elimination method will work best because both equations have a 2t term. If we subtract them, the t's will be eliminated and we can solve for s.

-4s = -16, so s = 4

Now you can substitute s = 4 into either equation and solve for t..

Once you have the ordered pair (s,t), that's where the lines intersect.