How Do I Solve Linear Equations with Fractions and Word Problems in Algebra?

[MATH DUMMY]

5X-5/2Y=-55
4X+2Y=-12
USE ADDITION METHOD...HOW I DO THIS PROBLEM THE FRACTIONS THROW ME OFF

ALSO
A VENDOR SELLS HOT DOGS AND BAGS OF CHIPS.A CUSTOMER BUYS 2 HOT DOGS AND 2 BAGS OF CHIPS FOR $7.00.ANOTHER CUSTOMER BUYS 4 HOT DOGS AND 5 BAGS OF CHIPS FOR $15.00.FIND THE COST OF EACH ITEM.

SOLVE:THE ANWSER IS $2.50 HOT DOGS AND CHIPS $1.00.

4x+3y=$12.25
2x+5y=$8.75
IS THAT HOW I SHOULD SET IT UP.THEN WHAT I DO?...SORRY MY NAME GOES PERFECT WITH THIS PROBLEM

 

[Quadratic]

5X-5/2Y=-55
4X+2Y=-12

You can just solve this by substitution. From the second equation:

4x+2y=-12
4x=-2y-12
2x=-y-6
y=(-2x-6)

So, you substitute that value in for y, and you get:

5x-(5/2)(-2x-6)=-55
5x-(-5x-15)=55
5x+5x+15=55
10x=40
x=4

Then, we replace x with 4, which gives us:

4(4)+2y=-12
16+12+2y=0
2y=-28
y=-14

So, x=4 and y=-14

ALSO
A VENDOR SELLS HOT DOGS AND BAGS OF CHIPS.A CUSTOMER BUYS 2 HOT DOGS AND 2 BAGS OF CHIPS FOR $7.00.ANOTHER CUSTOMER BUYS 4 HOT DOGS AND 5 BAGS OF CHIPS FOR $15.00.FIND THE COST OF EACH ITEM.

SOLVE:THE ANWSER IS $2.50 HOT DOGS AND CHIPS $1.00.

Correct.

4x+3y=$12.25
2x+5y=$8.75

Again, this is called "solving a system of equations". You can use all sorts of methods to solve this, including solvin by substitution (which I used for the first question), elimination (trying to combine the equations, making one variable cancel), and even matricies. I might elaborate in a bit, but I'm getting increasingly sleepy...