Find the cost of a pencil and eraser if two pencils and three erasers cost 140 dollars, and fivepencils and four erasers cost 280 dollars.
let's define a variable p for pencils and e for erasers.
now we can set up a sysem of equations.
2p + 3e = 140
5p + 4e = 280
for this problem, i'm going to use elimination.
we multiplfy the first equation by 5 and the second equation by 2.
10p + 15e = 700
10p + 8e = 560
notice how we now have a 10p on both equations. we can subtract the two equations to cancel those out.
7e = 700 - 560
7e = 140
e = 20
now we can solve for p.
2p + 3(20) = 140
2p + 60 = 140
2p = 80
p = 40
hope this helped! please let me know if you are confused about anything i did