Question

How do you create equations for this word problem?

You bought a total of 6 pens and pencils for $4. If each pen costs $1 and each pencil costs $.50, how many pens and pencils did you buy?

Answer 1

you could get it maybe just thinking about it from those easy numbers... but the way to do those types involves a system of 2 equations, so you can solve for #Pens and #Pencils

Answer 2

Relate the quantities in one equation, and the cost in the other

Answer 3

Would it be

1x + .50y = 4
x + y = 6

Answer 4

Define a couple variables for the quantity of each

Answer 5

ok so Pens are X since you have a dollar on that one

Answer 6

Yep

Answer 7

which way do you solve systems so far

Answer 8

substitute in a variable to reduce to a single variable equation?, by solving one for a variable, and sub that in to the second

Answer 9

yeah

Answer 10

have you done , adding equations together to eliminate a variable?

Answer 11

multiply one of the equations through by -1, then add them together, the x will go away

Answer 12

oh yeah i done that, but now i have to make an equation so i can graph them

Answer 13

i have to solve it by graphing now

Answer 14

graph both of the linear equations, since there is a solution here, they will intersect at one point (x,y)

Answer 15

Axis of Pens vs pencils

Answer 16

since both are in standard form now, you can just plot the axis intercepts and line through them, let x=0, solve y, let y=0, solve x

Answer 17

I got (7, -2), idk if i did it right